Question

Group of order greater than 8 doesn't decompose into a direct product and Sylow 2-subgroup isomorphic quaternion group

score 33 · Answer 1 · 2018-12-08 10:35:33

33

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Group of order greater than 8 doesn't decompose into a direct product and Sylow 2-subgroup isomorphic quaternion group

Published on 08 Dec 2018 - 10:35

score 49 · Answer 2 · 2018-12-08 21:29:58

49

Views

Group Theory Subgroups Sylow Theory

Published on 08 Dec 2018 - 21:29

score 128 · Answer 3 · 2026-03-25 01:38:05

128

Views

The cases in proving that a group of order 90 is not simple

Published on 25 Mar 2026 - 1:38

score 153 · Answer 4 · 2026-03-25 01:37:48

153

Views

No group of order 10000 is simple

Published on 25 Mar 2026 - 1:37

score 430 · Answer 5 · 2018-12-09 04:20:08

430

Views

Every Sylow subgroup is normal, then $G$ has a subgroup of order $m$ for every division $m$ of $|G|$

Published on 09 Dec 2018 - 4:20

score 60 · Answer 6 · 2018-12-10 00:23:59

60

Views

Group Theory Sylow Subgroup

Published on 10 Dec 2018 - 0:23

score 42 · Answer 7 · 2018-12-12 06:19:05

42

Views

G has 4-Sylow 3-subgroups

Published on 12 Dec 2018 - 6:19

score 38 · Answer 8 · 2018-12-13 03:55:03

38

Views

Number of proper nontrivial subgroups for a group $G$ with size $pq$?

Published on 13 Dec 2018 - 3:55

score 56 · Answer 9 · 2018-12-13 19:25:57

56

Views

In a group of order $m p^n$ for $p$ prime, if $k<n$, is there an element of order $p^k$?

Published on 13 Dec 2018 - 19:25

score 74 · Answer 10 · 2018-12-22 23:38:53

74

Views

a few questions about what's going on in this proof of sylow's theorem I found

Published on 22 Dec 2018 - 23:38

score 123 · Answer 11 · 2018-12-23 02:03:25

123

Views

trying to understand this proof of sylows theorem that say the number of p-sylow subgroups is 1+kp

Published on 23 Dec 2018 - 2:03

score 98 · Answer 12 · 2018-12-23 21:49:37

98

Views

How can $SN_G(D)=G$ if $S$ is not normal in $G$?

Published on 23 Dec 2018 - 21:49

score 92 · Answer 13 · 2026-03-25 08:14:04

92

Views

Show that any finite nilpotent group of square free order is cyclic.

Published on 25 Mar 2026 - 8:14

score 107 · Answer 14 · 2026-03-25 04:36:31

107

Views

Abelian normal subgroups of A-groups

Published on 25 Mar 2026 - 4:36

score 80 · Answer 15 · 2026-03-25 07:45:44

80

Views

If $P$ is a Sylow $p$-subgroup of $G$ then there exists a normal subgroup $K$ such that $G/K$ is isomorphic to $P/P \cap G'$

Published on 25 Mar 2026 - 7:45

List Question

Group of order greater than 8 doesn't decompose into a direct product and Sylow 2-subgroup isomorphic quaternion group

Group Theory Subgroups Sylow Theory

The cases in proving that a group of order 90 is not simple

No group of order 10000 is simple

Every Sylow subgroup is normal, then $G$ has a subgroup of order $m$ for every division $m$ of $|G|$

Group Theory Sylow Subgroup

G has 4-Sylow 3-subgroups

Number of proper nontrivial subgroups for a group $G$ with size $pq$?

In a group of order $m p^n$ for $p$ prime, if $k<n$, is there an element of order $p^k$?

a few questions about what's going on in this proof of sylow's theorem I found

trying to understand this proof of sylows theorem that say the number of p-sylow subgroups is 1+kp

How can $SN_G(D)=G$ if $S$ is not normal in $G$?

Show that any finite nilpotent group of square free order is cyclic.

Abelian normal subgroups of A-groups

If $P$ is a Sylow $p$-subgroup of $G$ then there exists a normal subgroup $K$ such that $G/K$ is isomorphic to $P/P \cap G'$

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