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Why is $G/ \ker f$ abelian?

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#abstract-algebra #general-topology #group-theory #abelian-groups
811
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How to prove finite abelian group is direct sum of cyclic groups by using matrices over Euclidean domain?

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#abstract-algebra #group-theory #ring-theory #modules #abelian-groups
130
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How impure can an impure subgroup be?

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#group-theory #abelian-groups
461
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Can non-abelian subgroups be found in abelian groups?

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#abstract-algebra #group-theory #abelian-groups
282
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Based on the following relations, calculate the abelian group with generators $x, y, z$ and $t$.

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#group-theory #modules #abelian-groups
72
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Number of characters II

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#abstract-algebra #abelian-groups #group-homomorphism #characters
756
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Subgroup of multiplicative group of integers mod n.

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#modular-arithmetic #abelian-groups #cyclic-groups
178
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Unique linear combination in an abelian group

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#abstract-algebra #group-theory #abelian-groups
242
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GAP — make an Additive Group into a Group

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#abelian-groups #gap
500
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$A$ is torsion free iff $Tor(A, B) = 0$ for all $B$ .

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#abstract-algebra #homological-algebra #abelian-groups
223
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Finite abelian group has a subgroup $H$ with cyclic quotient that "preserves" the order in the quotient.

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#group-theory #reference-request #abelian-groups #alternative-proof #sylow-theory
120
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Isomorphism between the groups $\mathbb Z/(a) \times \mathbb Z / (b)$ and $\mathbb Z/(m) \times \mathbb Z / (n) $

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#group-theory #modules #abelian-groups
485
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Tensor product of group algebras

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#group-theory #commutative-algebra #abelian-groups #group-rings
15
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how is the target of $\text{tor}_n^R(A,\ )$ related to $\mathbf{Ab}$?

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#abelian-groups #functors #derived-functors #torsion-groups
179
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the action of $\mathbb{Q}$ on the abelian group should be extended uniquely from $\mathbb Z$

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#vector-spaces #modules #abelian-groups

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