Recognise this Cayley table? Almost embedded +_2
up vote
0
down vote
favorite
Finding monoids represented by very simple string rewrite systems. Come to a monoid of the following form.
({0,1,2} , * )
Where * is the binary operation with the following Cayley table:
* 0 1 2
0 0 1 2
1 1 2 1
2 2 1 2
Does anyone recognise this Cayley table?
If it helps, I'd expect the next monoid in my generation, M = ({0,1,2,3}, *)
Where * is the bi.op with the Cayley table:
* 0 1 2 3
0 0 1 2 3
1 1 2 3 1
2 2 3 1 2
3 3 1 2 3
In general * for a Monoid, M=( A , *) where |A| = n
* 0 1 2 .. n-1
0 0 1 2 .. n-1
1 1 2 3 .. 1
2 2 3 4 .. 2
. . . . .
n-1 n-1 1 2 .. n-1
group-theory word-problem monoid
edited Nov 21 at 13:11
Nicky Hekster
28k53254
asked Nov 21 at 11:29
O.Gage
12
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
Finding monoids represented by very simple string rewrite systems. Come to a monoid of the following form.
({0,1,2} , * )
Where * is the binary operation with the following Cayley table:
* 0 1 2
0 0 1 2
1 1 2 1
2 2 1 2
Does anyone recognise this Cayley table?
If it helps, I'd expect the next monoid in my generation, M = ({0,1,2,3}, *)
Where * is the bi.op with the Cayley table:
* 0 1 2 3
0 0 1 2 3
1 1 2 3 1
2 2 3 1 2
3 3 1 2 3
In general * for a Monoid, M=( A , *) where |A| = n
* 0 1 2 .. n-1
0 0 1 2 .. n-1
1 1 2 3 .. 1
2 2 3 4 .. 2
. . . . .
n-1 n-1 1 2 .. n-1
group-theory word-problem monoid
edited Nov 21 at 13:11
Nicky Hekster
28k53254
asked Nov 21 at 11:29
O.Gage
12
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
The only question I can find in your post is "Does anyone recognise this kayley table?". Is that really what you wanted to find out?
– MJD
Nov 21 at 12:15
1
The nonzero elements form a submonoid isomorphic to the cyclic group of order $n$. So the monoid here is the cyclic group of order $n$ with a new identity element $0$ adjoined.
– Derek Holt
Nov 21 at 16:20
To clarify. I'm currently researching monoids which admit a presentation by a complete string rewriting system as to provide a solution to the word problem. Have produced the table from the s.r.s < a | { (aaaa, a) } >. In working through classes of string rewrite systems I've managed to find some nice paterns in the multiplication tables (probably a more correct term than Kayley table as we are outside group theory). Nice tables like modular addition have cropped up. Was wondering if this was a nice table with a name that anyone recognised.
– O.Gage
Nov 24 at 20:52
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Finding monoids represented by very simple string rewrite systems. Come to a monoid of the following form.
({0,1,2} , * )
Where * is the binary operation with the following Cayley table:
* 0 1 2
0 0 1 2
1 1 2 1
2 2 1 2
Does anyone recognise this Cayley table?
If it helps, I'd expect the next monoid in my generation, M = ({0,1,2,3}, *)
Where * is the bi.op with the Cayley table:
* 0 1 2 3
0 0 1 2 3
1 1 2 3 1
2 2 3 1 2
3 3 1 2 3
In general * for a Monoid, M=( A , *) where |A| = n
* 0 1 2 .. n-1
0 0 1 2 .. n-1
1 1 2 3 .. 1
2 2 3 4 .. 2
. . . . .
n-1 n-1 1 2 .. n-1
group-theory word-problem monoid
edited Nov 21 at 13:11
Nicky Hekster
28k53254
asked Nov 21 at 11:29
O.Gage
12
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Finding monoids represented by very simple string rewrite systems. Come to a monoid of the following form.
({0,1,2} , * )
Where * is the binary operation with the following Cayley table:
* 0 1 2
0 0 1 2
1 1 2 1
2 2 1 2
Does anyone recognise this Cayley table?
If it helps, I'd expect the next monoid in my generation, M = ({0,1,2,3}, *)
Where * is the bi.op with the Cayley table:
* 0 1 2 3
0 0 1 2 3
1 1 2 3 1
2 2 3 1 2
3 3 1 2 3
In general * for a Monoid, M=( A , *) where |A| = n
* 0 1 2 .. n-1
0 0 1 2 .. n-1
1 1 2 3 .. 1
2 2 3 4 .. 2
. . . . .
n-1 n-1 1 2 .. n-1
group-theory word-problem monoid
group-theory word-problem monoid
edited Nov 21 at 13:11
Nicky Hekster
28k53254
asked Nov 21 at 11:29
O.Gage
12
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 21 at 13:11
Nicky Hekster
28k53254
asked Nov 21 at 11:29
O.Gage
12
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 21 at 13:11
Nicky Hekster
28k53254
edited Nov 21 at 13:11
Nicky Hekster
28k53254
edited Nov 21 at 13:11
Nicky Hekster
28k53254
28k53254
asked Nov 21 at 11:29
O.Gage
12
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 21 at 11:29
O.Gage
12
asked Nov 21 at 11:29
O.Gage
12
12
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
O.Gage is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
The only question I can find in your post is "Does anyone recognise this kayley table?". Is that really what you wanted to find out?
– MJD
Nov 21 at 12:15
1
The nonzero elements form a submonoid isomorphic to the cyclic group of order $n$. So the monoid here is the cyclic group of order $n$ with a new identity element $0$ adjoined.
– Derek Holt
Nov 21 at 16:20
To clarify. I'm currently researching monoids which admit a presentation by a complete string rewriting system as to provide a solution to the word problem. Have produced the table from the s.r.s < a | { (aaaa, a) } >. In working through classes of string rewrite systems I've managed to find some nice paterns in the multiplication tables (probably a more correct term than Kayley table as we are outside group theory). Nice tables like modular addition have cropped up. Was wondering if this was a nice table with a name that anyone recognised.
– O.Gage
Nov 24 at 20:52
add a comment |
2
The only question I can find in your post is "Does anyone recognise this kayley table?". Is that really what you wanted to find out?
– MJD
Nov 21 at 12:15
1
The nonzero elements form a submonoid isomorphic to the cyclic group of order $n$. So the monoid here is the cyclic group of order $n$ with a new identity element $0$ adjoined.
– Derek Holt
Nov 21 at 16:20
To clarify. I'm currently researching monoids which admit a presentation by a complete string rewriting system as to provide a solution to the word problem. Have produced the table from the s.r.s < a | { (aaaa, a) } >. In working through classes of string rewrite systems I've managed to find some nice paterns in the multiplication tables (probably a more correct term than Kayley table as we are outside group theory). Nice tables like modular addition have cropped up. Was wondering if this was a nice table with a name that anyone recognised.
– O.Gage
Nov 24 at 20:52
2
2
The only question I can find in your post is "Does anyone recognise this kayley table?". Is that really what you wanted to find out?
– MJD
Nov 21 at 12:15
The only question I can find in your post is "Does anyone recognise this kayley table?". Is that really what you wanted to find out?
– MJD
Nov 21 at 12:15
1
1
The nonzero elements form a submonoid isomorphic to the cyclic group of order $n$. So the monoid here is the cyclic group of order $n$ with a new identity element $0$ adjoined.
– Derek Holt
Nov 21 at 16:20
The nonzero elements form a submonoid isomorphic to the cyclic group of order $n$. So the monoid here is the cyclic group of order $n$ with a new identity element $0$ adjoined.
– Derek Holt
Nov 21 at 16:20
To clarify. I'm currently researching monoids which admit a presentation by a complete string rewriting system as to provide a solution to the word problem. Have produced the table from the s.r.s < a | { (aaaa, a) } >. In working through classes of string rewrite systems I've managed to find some nice paterns in the multiplication tables (probably a more correct term than Kayley table as we are outside group theory). Nice tables like modular addition have cropped up. Was wondering if this was a nice table with a name that anyone recognised.
– O.Gage
Nov 24 at 20:52
To clarify. I'm currently researching monoids which admit a presentation by a complete string rewriting system as to provide a solution to the word problem. Have produced the table from the s.r.s < a | { (aaaa, a) } >. In working through classes of string rewrite systems I've managed to find some nice paterns in the multiplication tables (probably a more correct term than Kayley table as we are outside group theory). Nice tables like modular addition have cropped up. Was wondering if this was a nice table with a name that anyone recognised.
– O.Gage
Nov 24 at 20:52
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
O.Gage is a new contributor. Be nice, and check out our Code of Conduct.
draft saved
draft discarded
O.Gage is a new contributor. Be nice, and check out our Code of Conduct.
O.Gage is a new contributor. Be nice, and check out our Code of Conduct.
O.Gage is a new contributor. Be nice, and check out our Code of Conduct.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3007597%2frecognise-this-cayley-table-almost-embedded-2%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
The only question I can find in your post is "Does anyone recognise this kayley table?". Is that really what you wanted to find out?
– MJD
Nov 21 at 12:15
1
The nonzero elements form a submonoid isomorphic to the cyclic group of order $n$. So the monoid here is the cyclic group of order $n$ with a new identity element $0$ adjoined.
– Derek Holt
Nov 21 at 16:20
To clarify. I'm currently researching monoids which admit a presentation by a complete string rewriting system as to provide a solution to the word problem. Have produced the table from the s.r.s < a | { (aaaa, a) } >. In working through classes of string rewrite systems I've managed to find some nice paterns in the multiplication tables (probably a more correct term than Kayley table as we are outside group theory). Nice tables like modular addition have cropped up. Was wondering if this was a nice table with a name that anyone recognised.
– O.Gage
Nov 24 at 20:52