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A subgroup $H$ of an abelian group $G$ is a direct summand iff $G/H$ is free?

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#group-theory #abelian-groups #direct-sum #free-groups
179
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subgroups of $\bigoplus_{i=-\infty}^{\infty}\mathbb{Z}_{(i)}$

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#abstract-algebra #group-theory #reference-request #abelian-groups #direct-sum
71
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Maximal subgroup disjoint with rationals

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#abstract-algebra #group-theory #modules #direct-sum
80
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generators of subgroups of $\bigoplus_{i=-\infty}^{\infty}\mathbb{Z}_{(i)}$

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#abstract-algebra #group-theory #elementary-number-theory #abelian-groups #direct-sum
67
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Does the subspace $W'$ exist such that $\mathbb{R}^3=W\oplus W'$?

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#linear-algebra #eigenvalues-eigenvectors #linear-transformations #direct-sum #invariant-subspace
103
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Question about proof of problem 10.3.21 in Dummit and Foote.

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#abstract-algebra #solution-verification #modules #direct-sum
86
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What is ${\rm Aut}\bigoplus_{i=-\infty}^{\infty}\mathbb{Z}_p$?

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#abstract-algebra #group-theory #abelian-groups #automorphism-group #direct-sum
73
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A "simpler" description of the automorphism group of the Lamplighter group

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#abstract-algebra #group-theory #abelian-groups #automorphism-group #direct-sum
71
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abelianization of the lamplighter group

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#abstract-algebra #group-theory #solution-verification #direct-sum #geometric-group-theory
128
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Is it possible to write a code that computes all the subgroups (up to isomorphism) of a finite Abelian group?

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#abstract-algebra #group-theory #abelian-groups #direct-sum #gap
65
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An analogous equivalence to one of linear independence

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#linear-algebra #vector-spaces #direct-sum #linear-independence
135
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Every complemented subspace has a non topological algebraic complement

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#functional-analysis #direct-sum #hahn-banach-theorem
47
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Finding space to solve direct sum equation

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#linear-algebra #direct-sum
94
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Question about the group algebra

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#abstract-algebra #group-theory #modules #representation-theory #direct-sum
70
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Quotient of the group $\mathbb{Z}^2 \oplus \mathbb{Z} ^2 \oplus \mathbb{Z} ^2$

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#abstract-algebra #group-theory #abelian-groups #direct-sum #quotient-group

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