Question

Let $G$ be a group of order $27$ that acts on a set $X$ with $135$ elements. Prove for each $x_1,x_2\in X,{\rm Stab}_G(x_1)={\rm Stab}_G(x_2)$.

score 78 · Answer 1 · 2021-08-29 19:43:00

78

Views

Let $G$ be a group of order $27$ that acts on a set $X$ with $135$ elements. Prove for each $x_1,x_2\in X,{\rm Stab}_G(x_1)={\rm Stab}_G(x_2)$.

Published on 29 Aug 2021 - 19:43

score 380 · Answer 2 · 2021-09-01 17:28:19

380

Views

Is a product of $p$-subgroups still a $p$-subgroup?

Published on 01 Sep 2021 - 17:28

score 117 · Answer 3 · 2026-03-28 02:05:22

117

Views

Show that a group, given by a presentation, is countable & reduced with a nontrivial element of infinite height

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score 118 · Answer 4 · 2021-09-09 19:03:15

118

Views

An abelian $p$-group has a bounded basic subgroup iff it is the direct sum of a divisible group and bounded group

Published on 09 Sep 2021 - 19:03

score 225 · Answer 5 · 2021-09-10 08:14:00

225

Views

Definition of special $p$-groups

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score 144 · Answer 6 · 2026-03-22 06:03:53

144

Views

The commutator subgroup of finite metabelian p-group

Published on 22 Mar 2026 - 6:03

score 70 · Answer 7 · 2021-09-21 21:39:30

70

Views

Suppose $M\leq P$ such that $|M|=p^m$, and both $M$ and $P/M$ are cyclic, then there exists $N\leq P$ such that $P=M+N$ and $M\cap N=\{0\}$.

Published on 21 Sep 2021 - 21:39

score 70 · Answer 8 · 2021-09-27 03:54:26

70

Views

Subgroups lattices of groups of order $p^3$

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score 39 · Answer 9 · 2026-02-23 07:41:22

39

Views

Information about $P'$ in $P \rtimes Q$

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score 41 · Answer 10 · 2021-10-01 12:22:05

41

Views

Size of normalizer of abelian subgroup of a $p$-group

Published on 01 Oct 2021 - 12:22

score 157 · Answer 11 · 2026-02-23 06:20:31

157

Views

An abelian torsion group has a unique basic subgroup iff it is divisible or bounded.

Published on 23 Feb 2026 - 6:20

score 70 · Answer 12 · 2026-03-25 10:54:13

70

Views

The Automorphisms of a group with a certain presentation

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score 33 · Answer 13 · 2021-10-12 02:50:18

Prove the order of $h$ when $h \in G\ \langle g \rangle$, $G$ is a finite abelian $p$-group that is not cyclic

score 48 · Answer 14 · 2026-03-25 23:56:39

48

Views

More convenient GAP code to verify Additional property of d-maximal groups

Published on 25 Mar 2026 - 23:56

score 47 · Answer 15 · 2021-10-27 08:42:11

47

Views

If $G=p^n$, how does the action of $\operatorname{Aut}(G)$ on $G/G'G^p$ induce a homomorphism $\operatorname{Aut}(G)\to GL_m(\mathbb{F}_p)$?

Published on 27 Oct 2021 - 8:42

List Question

Let $G$ be a group of order $27$ that acts on a set $X$ with $135$ elements. Prove for each $x_1,x_2\in X,{\rm Stab}_G(x_1)={\rm Stab}_G(x_2)$.

Is a product of $p$-subgroups still a $p$-subgroup?

Show that a group, given by a presentation, is countable & reduced with a nontrivial element of infinite height

An abelian $p$-group has a bounded basic subgroup iff it is the direct sum of a divisible group and bounded group

Definition of special $p$-groups

The commutator subgroup of finite metabelian p-group

Suppose $M\leq P$ such that $|M|=p^m$, and both $M$ and $P/M$ are cyclic, then there exists $N\leq P$ such that $P=M+N$ and $M\cap N=\{0\}$.

Subgroups lattices of groups of order $p^3$

Information about $P'$ in $P \rtimes Q$

Size of normalizer of abelian subgroup of a $p$-group

An abelian torsion group has a unique basic subgroup iff it is divisible or bounded.

The Automorphisms of a group with a certain presentation

Prove the order of $h$ when $h \in G\ \langle g \rangle$, $G$ is a finite abelian $p$-group that is not cyclic

More convenient GAP code to verify Additional property of d-maximal groups

If $G=p^n$, how does the action of $\operatorname{Aut}(G)$ on $G/G'G^p$ induce a homomorphism $\operatorname{Aut}(G)\to GL_m(\mathbb{F}_p)$?

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