Question

If a group $G \cong H$, and if $H$ is a simple group, is $G$ also a simple group?

score 118 · Answer 1 · 2026-04-12 00:36:40

118

Views

If a group $G \cong H$, and if $H$ is a simple group, is $G$ also a simple group?

Published on 12 Apr 2026 - 0:36

score 110 · Answer 2 · 2026-03-26 04:28:55

110

Views

Simple groups satisfying some conditions

Published on 26 Mar 2026 - 4:28

score 53 · Answer 3 · 2026-04-10 15:05:05

53

Views

Is it possible to take a power series expansion "in the monster group"

Published on 10 Apr 2026 - 15:05

score 88 · Answer 4 · 2026-05-11 02:01:53

88

Views

Extensions of $A_5$ by $C_2$.

Published on 11 May 2026 - 2:01

score 90 · Answer 5 · 2026-04-13 12:49:18

90

Views

Does there exist a two-generated simple non-abelian group with specific properties?

Published on 13 Apr 2026 - 12:49

score 101 · Answer 6 · 2026-04-10 03:06:38

101

Views

Two questions about non-abelian finite simple groups

Published on 10 Apr 2026 - 3:06

score 745 · Answer 7 · 2026-04-14 07:08:23

745

Views

Reference request: a list of (small) finite simple groups

Published on 14 Apr 2026 - 7:08

score 286 · Answer 8 · 2026-04-16 12:19:28

286

Views

Prove that there is no simple group of order $216=2^{3}\cdot 3^{3}$.

Published on 16 Apr 2026 - 12:19

score 77 · Answer 9 · 2026-04-15 10:42:06

Elementary (CFSG-avoiding) proof that the order of a group of composite order is bounded by the square of the order of its largest proper subgroup?

score 990 · Answer 10 · 2026-04-17 00:44:32

990

Views

Simple group of order $p^2 q r$, where $p, q, r$ are distinct primes, is isomorphic to $A_5$

Published on 17 Apr 2026 - 0:44

score 180 · Answer 11 · 2026-04-15 20:40:11

180

Views

Let $G$ be a simple group. Show that if $H$ is a subgroup $G$ such that $[G:H]= 3$ then $H=\{1\}$ and $|G|=3$.

Published on 15 Apr 2026 - 20:40

score 65 · Answer 12 · 2026-04-16 00:17:15

65

Views

On the intersections of maximal subgroups of finite simple groups

Published on 16 Apr 2026 - 0:17

score 624 · Answer 13 · 2026-04-12 05:58:06

624

Views

How do we compute the order of the Monster group?

Published on 12 Apr 2026 - 5:58

score 96 · Answer 14 · 2026-04-13 16:27:50

96

Views

Show there are are no simple groups of order 1638

Published on 13 Apr 2026 - 16:27

score 95 · Answer 15 · 2026-04-15 20:38:06

95

Views

Let be $A_n$ the alternating group $n\geq 5$. How to prove that $\operatorname{Stab}_{A_n}(x) \cong A_{n-1}$, for all $x \in \{1, ..., n\}$?

Published on 15 Apr 2026 - 20:38

List Question

If a group $G \cong H$, and if $H$ is a simple group, is $G$ also a simple group?

Simple groups satisfying some conditions

Is it possible to take a power series expansion "in the monster group"

Extensions of $A_5$ by $C_2$.

Does there exist a two-generated simple non-abelian group with specific properties?

Two questions about non-abelian finite simple groups

Reference request: a list of (small) finite simple groups

Prove that there is no simple group of order $216=2^{3}\cdot 3^{3}$.

Elementary (CFSG-avoiding) proof that the order of a group of composite order is bounded by the square of the order of its largest proper subgroup?

Simple group of order $p^2 q r$, where $p, q, r$ are distinct primes, is isomorphic to $A_5$

Let $G$ be a simple group. Show that if $H$ is a subgroup $G$ such that $[G:H]= 3$ then $H=\{1\}$ and $|G|=3$.

On the intersections of maximal subgroups of finite simple groups

How do we compute the order of the Monster group?

Show there are are no simple groups of order 1638

Let be $A_n$ the alternating group $n\geq 5$. How to prove that $\operatorname{Stab}_{A_n}(x) \cong A_{n-1}$, for all $x \in \{1, ..., n\}$?

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