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Decomposition of finite abelian $p$-group into cyclic groups is unique. "Simpler" proof?

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#abstract-algebra #group-theory #finite-groups #abelian-groups
80
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Nonisomorphic Groups with the Same Order and Exponent

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#finite-groups #examples-counterexamples #abelian-groups
124
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Is it necessary for this abelian group to have $4n+2$?

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#abstract-algebra #group-theory #proof-verification #finite-groups #abelian-groups
139
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Abelian Group Criteria and counterexample

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#group-theory #abelian-groups
54
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Showing $A= A_r \bigoplus A_s$

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#group-theory #proof-verification #abelian-groups #direct-sum
428
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The Isomorphism for Smith Normal Form

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#linear-algebra #abstract-algebra #group-theory #finite-groups #abelian-groups
467
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When the derived (commutator) subgroup is in the center

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#group-theory #abelian-groups #normal-subgroups #quotient-group
292
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Conjugacy classes in virtually nilpotent groups

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#group-theory #abelian-groups #nilpotent-groups
1.2k
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On the inclusion homomorphism $\mathbb Z\to\mathbb Q$

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#abstract-algebra #group-theory #category-theory #abelian-groups #group-homomorphism
259
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Is there a natural example of a divisible torsioned (= periodic) abelian group?

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#abstract-algebra #group-theory #logic #model-theory #abelian-groups
113
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Number of homomorphisms/characters

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#abstract-algebra #abelian-groups #group-homomorphism #characters
58
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Invariant basis of some free $\mathbb{Z}$-module

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#abelian-groups #group-actions #invariant-subspace #free-abelian-group
119
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Prove: $ (G^{S},*)$ is abelian group if and only if $(G,\cdot )$ is abelian.

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#group-theory #abelian-groups
219
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Groups: Restrictions Necessary For Closure Under Multiplication?

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#abstract-algebra #group-theory #abelian-groups
126
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Challenge: find the order of an element in a Finite Abelian Group with a given presentation

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#matrices #finite-groups #abelian-groups #group-presentation

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