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Show $a\in G$ is contained in $Z(G)$ iff $Z(a)=G$ for center and centralizer?

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#abstract-algebra #group-theory #abelian-groups
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Direct sum and direct product of infinitely many abelian groups are not isomorphic

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$G$ infinite abelian group with $[G:H]$ finite for every non trivial subgroup $H$ , to prove $G$ is cyclic

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#group-theory #abelian-groups #cyclic-groups #infinite-groups #abstract-algebra
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Least common multiple of orders and abelian groups.

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#abstract-algebra #group-theory #abelian-groups
322
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Irreducible subgroups of the additive rationals

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#abstract-algebra #group-theory #abelian-groups #divisible-groups
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|ab|=lcm(|a|,|b|) in an abelian group

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#abstract-algebra #group-theory #finite-groups #abelian-groups #least-common-multiple
343
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Can we calculate the order of $\hom (G,G')$ in terms of $|G| $ and $ |G'|$ , when $G,G'$ are finite abelian groups?

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#group-theory #finite-groups #abelian-groups #abstract-algebra
79
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Description of an abelian group

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#abstract-algebra #finite-groups #abelian-groups
125
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Order of the group.

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#group-theory #finite-groups #abelian-groups
70
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Abelian Group (Alternative Proof)

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#abstract-algebra #group-theory #self-learning #abelian-groups #alternative-proof
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How many distinct subgroups of order 10 are there in a non-cyclic abelian group of order 20?

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#abstract-algebra #group-theory #finite-groups #abelian-groups
3.1k
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Automorphism iff G is abelian

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#abstract-algebra #abelian-groups
182
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homomorphisms of abelian groups

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#abelian-groups
472
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Is every free subgroup a direct summand?

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#abstract-algebra #group-theory #abelian-groups
104
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Finite Abelian Group Proof

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#abstract-algebra #abelian-groups

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