Question

If every finite quotient group of a finitely generated linear group G is solvable, then G is solvable

score 242 · Answer 1 · 2026-03-27 04:38:10

242

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If every finite quotient group of a finitely generated linear group G is solvable, then G is solvable

Published on 27 Mar 2026 - 4:38

score 41 · Answer 2 · 2022-01-17 16:40:02

41

Views

If $\langle x \rangle =_{df} H(\{x\})$ with $H(S) , (S $ a set $)$ as defined below , how can $\langle x \rangle$ have more than $3$ elements?

Published on 17 Jan 2022 - 16:40

score 117 · Answer 3 · 2026-03-26 04:31:57

117

Views

If $A\ast_C B$ is finitely generated, are $A$ and $B$ finitely generated?

Published on 26 Mar 2026 - 4:31

score 87 · Answer 4 · 2026-03-27 10:45:50

87

Views

Two Properties of Perfect Rings

Published on 27 Mar 2026 - 10:45

score 328 · Answer 5 · 2022-01-29 00:42:26

328

Views

Finitely generated $R$-module that is not projective or finitely presented

Published on 29 Jan 2022 - 0:42

score 28 · Answer 6 · 2022-01-29 17:09:20

28

Views

Is $\ker(f)$ a finitely generated sub-module of $M$ if $\ker(f)\cong M/f(M),f\in \text{End}_R(M)$?

Published on 29 Jan 2022 - 17:09

score 41 · Answer 7 · 2026-03-27 23:14:20

41

Views

Do images and kernels of invariant modules have the form $Mr$ and $\text{Ann}(r)$ respectively for some $r\in R$?

Published on 27 Mar 2026 - 23:14

score 187 · Answer 8 · 2026-03-30 04:56:43

187

Views

A group is locally free exactly when its finitely generated subgroups are free

Published on 30 Mar 2026 - 4:56

score 34 · Answer 9 · 2026-03-30 00:19:28

34

Views

$M$ finitely generated $\nRightarrow$ $N$ and $M/N$ finitely generated

Published on 30 Mar 2026 - 0:19

score 42 · Answer 10 · 2022-02-03 13:12:48

42

Views

Is the sum of abelian cyclic modules abelian?

Published on 03 Feb 2022 - 13:12

score 88 · Answer 11 · 2026-03-27 21:54:27

88

Views

A characterisation of flatness

Published on 27 Mar 2026 - 21:54

score 49 · Answer 12 · 2022-02-09 08:16:10

49

Views

Equivalent condition for uniserial torsion module over a PID

Published on 09 Feb 2022 - 8:16

score 91 · Answer 13 · 2022-02-10 09:35:15

91

Views

$p$-adic topology on a finitely generated module

Published on 10 Feb 2022 - 9:35

score 139 · Answer 14 · 2026-03-25 06:04:28

139

Views

Change of rings of scalars and projecivity?

Published on 25 Mar 2026 - 6:04

score 93 · Answer 15 · 2022-02-17 02:07:50

93

Views

Efficient way to define generating of finite groups

Published on 17 Feb 2022 - 2:07

List Question

If every finite quotient group of a finitely generated linear group G is solvable, then G is solvable

If $\langle x \rangle =_{df} H(\{x\})$ with $H(S) , (S $ a set $)$ as defined below , how can $\langle x \rangle$ have more than $3$ elements?

If $A\ast_C B$ is finitely generated, are $A$ and $B$ finitely generated?

Two Properties of Perfect Rings

Finitely generated $R$-module that is not projective or finitely presented

Is $\ker(f)$ a finitely generated sub-module of $M$ if $\ker(f)\cong M/f(M),f\in \text{End}_R(M)$?

Do images and kernels of invariant modules have the form $Mr$ and $\text{Ann}(r)$ respectively for some $r\in R$?

A group is locally free exactly when its finitely generated subgroups are free

$M$ finitely generated $\nRightarrow$ $N$ and $M/N$ finitely generated

Is the sum of abelian cyclic modules abelian?

A characterisation of flatness

Equivalent condition for uniserial torsion module over a PID

$p$-adic topology on a finitely generated module

Change of rings of scalars and projecivity?

Efficient way to define generating of finite groups

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