List questions from exact-sequence

Published on 25 Mar 2026 - 22:09

50

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$0 \to G' \xrightarrow{\alpha} G \xrightarrow{\beta} G'' \to 0$ exact sequence, $G$ is torsion group if and only if $G'$ and $G''$ are torsion groups.

Published on 26 Mar 2026 - 19:19

587

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Any reference for induces exact sequence $0 \to Ker(f) \to Ker(gf) \to Ker(g) \xrightarrow{\delta} Coker(f) \to Coker(gf) \to Coker(g) \to 0.$

Published on 21 Nov 2020 - 16:55

54

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Condition for an element in Ext be zero

Published on 24 Nov 2020 - 18:47

151

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Having trouble understanding nilpotent and supersolvable group in terms of short exact sequence

Published on 25 Mar 2026 - 22:04

53

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Exact sequence, coequalizer and existence of a morphism

Published on 01 Dec 2020 - 9:28

99

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Short exact sequence of groups acting on a space

Published on 23 Feb 2026 - 6:21

94

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Definition of $I(\varphi, M)$ in Buchsbaum's and Eisenbud's "What makes a complex exact?"

Published on 02 Dec 2020 - 16:05

865

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Is an group determined by its torsion part and torsion-free part?

Published on 26 Mar 2026 - 22:58

210

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The proof of the kernel and cokernel formula of a certain map.

Published on 06 Dec 2020 - 1:14

105

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Long exact sequence in homology of a $3$-manifold with nonconnected boundary

Published on 08 Dec 2020 - 0:51

48

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Exact sequence of 4 abelian groups, 3 of them being free

Published on 29 Mar 2026 - 20:16

573

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Does a cokernel in a exact sequence induce a monomorphism?

Published on 09 Dec 2020 - 12:06

280

Views

Nilpotent groups can be constructed by means of abelian groups.

Published on 25 Mar 2026 - 4:40

482

Views

Maps in the long exact sequence of relative homology groups

Published on 09 Dec 2020 - 18:53

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Semidirect product is supersolvable groups

$0 \to G' \xrightarrow{\alpha} G \xrightarrow{\beta} G'' \to 0$ exact sequence, $G$ is torsion group if and only if $G'$ and $G''$ are torsion groups.

Any reference for induces exact sequence $0 \to Ker(f) \to Ker(gf) \to Ker(g) \xrightarrow{\delta} Coker(f) \to Coker(gf) \to Coker(g) \to 0.$

Condition for an element in Ext be zero

Having trouble understanding nilpotent and supersolvable group in terms of short exact sequence

Exact sequence, coequalizer and existence of a morphism

Short exact sequence of groups acting on a space

Definition of $I(\varphi, M)$ in Buchsbaum's and Eisenbud's "What makes a complex exact?"

Is an group determined by its torsion part and torsion-free part?

The proof of the kernel and cokernel formula of a certain map.

Long exact sequence in homology of a $3$-manifold with nonconnected boundary

Exact sequence of 4 abelian groups, 3 of them being free

Does a cokernel in a exact sequence induce a monomorphism?

Nilpotent groups can be constructed by means of abelian groups.

Maps in the long exact sequence of relative homology groups

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