Question

Suppose $f:G\longrightarrow H$ is a group homomorphism with $H$, $Ker(f)$ finite. Is $G$ finite?

score 435 · Answer 1 · 2018-11-07 21:40:33

435

Views

Suppose $f:G\longrightarrow H$ is a group homomorphism with $H$, $Ker(f)$ finite. Is $G$ finite?

Published on 07 Nov 2018 - 21:40

score 459 · Answer 2 · 2026-03-25 06:07:02

459

Views

What's an example of a finite, non-abelian, non-simple group that is not semidirectly reducible?

Published on 25 Mar 2026 - 6:07

score 190 · Answer 3 · 2026-03-25 15:51:48

190

Views

The automorphism group of $S_6$ is isomorphic to a semidirect prodct

Published on 25 Mar 2026 - 15:51

score 125 · Answer 4 · 2018-11-08 05:54:34

125

Views

Example of group of order $216$ with a property

Published on 08 Nov 2018 - 5:54

score 136 · Answer 5 · 2026-03-25 15:51:52

136

Views

Solvability of the (outer) automorphism group of a central product

Published on 25 Mar 2026 - 15:51

score 124 · Answer 6 · 2026-03-26 05:55:59

124

Views

Are groups of order $p^2$ abelian, $p$ prime?

Published on 26 Mar 2026 - 5:55

score 137 · Answer 7 · 2026-03-25 17:35:24

137

Views

Normal subgroup generated by $D_8$

Published on 25 Mar 2026 - 17:35

score 225 · Answer 8 · 2026-03-27 02:59:44

225

Views

Group Theory greatest common divisor and order

Published on 27 Mar 2026 - 2:59

score 668 · Answer 9 · 2018-11-09 04:31:49

668

Views

Find subgroups of $D_4$.

Published on 09 Nov 2018 - 4:31

score 413 · Answer 10 · 2026-03-25 09:34:45

413

Views

Are any two distinct p-Sylow subgroups normal?

Published on 25 Mar 2026 - 9:34

score 78 · Answer 11 · 2026-03-25 09:37:15

78

Views

Help me to better understand the intersection of Sylow $p$-subgroups?

Published on 25 Mar 2026 - 9:37

score 199 · Answer 12 · 2026-03-25 09:43:49

199

Views

Does the centraliser of the intersection of any two Sylow $p$-subgroups contain all Sylow $p$-subgroups?

Published on 25 Mar 2026 - 9:43

score 1.9k · Answer 13 · 2018-11-10 06:24:34

1.9k

Views

If every proper subgroup of a finite abelian group $G$ is cyclic, then $G$ is cyclic.

Published on 10 Nov 2018 - 6:24

score 75 · Answer 14 · 2018-11-10 12:02:18

75

Views

Does $g^{k} x h^{k} = x$ for all $k \geq 1$ imply $g = h^{-1}$ and $gx = xg$?

Published on 10 Nov 2018 - 12:02

score 107 · Answer 15 · 2026-03-25 23:42:45

107

Views

Order of $Z^1(G,A)$, the group of $1$-cocycles, when both $G$ and $A$ are finite

Published on 25 Mar 2026 - 23:42

List Question

Suppose $f:G\longrightarrow H$ is a group homomorphism with $H$, $Ker(f)$ finite. Is $G$ finite?

What's an example of a finite, non-abelian, non-simple group that is not semidirectly reducible?

The automorphism group of $S_6$ is isomorphic to a semidirect prodct

Example of group of order $216$ with a property

Solvability of the (outer) automorphism group of a central product

Are groups of order $p^2$ abelian, $p$ prime?

Normal subgroup generated by $D_8$

Group Theory greatest common divisor and order

Find subgroups of $D_4$.

Are any two distinct p-Sylow subgroups normal?

Help me to better understand the intersection of Sylow $p$-subgroups?

Does the centraliser of the intersection of any two Sylow $p$-subgroups contain all Sylow $p$-subgroups?

If every proper subgroup of a finite abelian group $G$ is cyclic, then $G$ is cyclic.

Does $g^{k} x h^{k} = x$ for all $k \geq 1$ imply $g = h^{-1}$ and $gx = xg$?

Order of $Z^1(G,A)$, the group of $1$-cocycles, when both $G$ and $A$ are finite

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