Show that any finite nilpotent group of square free order is cyclic.
$begingroup$
Show that any finite nilpotent group of square free order is cyclic.
Hint: Suppose G is such a group. Any Sylow subgroup of G is of prime order.
Hint: Any finite nilpotent group is the direct product of its Sylow subgroups.
Hint: Use the Chinese Remainder Theorem.
Any idea,
abstract-algebra group-theory cyclic-groups sylow-theory nilpotent-groups
edited Dec 24 '18 at 13:12
Shaun
9,380113684
asked Dec 24 '18 at 3:45
NawalNawal
223
$endgroup$
add a comment |
$begingroup$
Show that any finite nilpotent group of square free order is cyclic.
Hint: Suppose G is such a group. Any Sylow subgroup of G is of prime order.
Hint: Any finite nilpotent group is the direct product of its Sylow subgroups.
Hint: Use the Chinese Remainder Theorem.
Any idea,
abstract-algebra group-theory cyclic-groups sylow-theory nilpotent-groups
edited Dec 24 '18 at 13:12
Shaun
9,380113684
asked Dec 24 '18 at 3:45
NawalNawal
223
$endgroup$
2
$begingroup$
Ii think those hints are aplenty. Just mimick the proof of $C_3times C_5simeq C_{15}$.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:45
$begingroup$
Also, I recommend that you take a look at our guide for new askers.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:46
add a comment |
$begingroup$
Show that any finite nilpotent group of square free order is cyclic.
Hint: Suppose G is such a group. Any Sylow subgroup of G is of prime order.
Hint: Any finite nilpotent group is the direct product of its Sylow subgroups.
Hint: Use the Chinese Remainder Theorem.
Any idea,
abstract-algebra group-theory cyclic-groups sylow-theory nilpotent-groups
edited Dec 24 '18 at 13:12
Shaun
9,380113684
asked Dec 24 '18 at 3:45
NawalNawal
223
$endgroup$
Show that any finite nilpotent group of square free order is cyclic.
Hint: Suppose G is such a group. Any Sylow subgroup of G is of prime order.
Hint: Any finite nilpotent group is the direct product of its Sylow subgroups.
Hint: Use the Chinese Remainder Theorem.
Any idea,
abstract-algebra group-theory cyclic-groups sylow-theory nilpotent-groups
abstract-algebra group-theory cyclic-groups sylow-theory nilpotent-groups
edited Dec 24 '18 at 13:12
Shaun
9,380113684
asked Dec 24 '18 at 3:45
NawalNawal
223
edited Dec 24 '18 at 13:12
Shaun
9,380113684
asked Dec 24 '18 at 3:45
NawalNawal
223
edited Dec 24 '18 at 13:12
Shaun
9,380113684
edited Dec 24 '18 at 13:12
Shaun
9,380113684
edited Dec 24 '18 at 13:12
Shaun
9,380113684
9,380113684
asked Dec 24 '18 at 3:45
NawalNawal
223
asked Dec 24 '18 at 3:45
NawalNawal
223
asked Dec 24 '18 at 3:45
NawalNawal
223
223
2
$begingroup$
Ii think those hints are aplenty. Just mimick the proof of $C_3times C_5simeq C_{15}$.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:45
$begingroup$
Also, I recommend that you take a look at our guide for new askers.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:46
add a comment |
2
$begingroup$
Ii think those hints are aplenty. Just mimick the proof of $C_3times C_5simeq C_{15}$.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:45
$begingroup$
Also, I recommend that you take a look at our guide for new askers.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:46
2
2
$begingroup$
Ii think those hints are aplenty. Just mimick the proof of $C_3times C_5simeq C_{15}$.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:45
$begingroup$
Ii think those hints are aplenty. Just mimick the proof of $C_3times C_5simeq C_{15}$.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:45
$begingroup$
Also, I recommend that you take a look at our guide for new askers.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:46
$begingroup$
Also, I recommend that you take a look at our guide for new askers.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:46
add a comment |
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$begingroup$
Ii think those hints are aplenty. Just mimick the proof of $C_3times C_5simeq C_{15}$.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:45
$begingroup$
Also, I recommend that you take a look at our guide for new askers.
$endgroup$
– Jyrki Lahtonen
Dec 24 '18 at 4:46