Tagged Questions
4
votes
1answer
111 views
Commutative ring and its group-algebra, and abelian-group-algebra as a commutative ring.
In course of discussing the algebraic structures, one of my seniors is led quite naturally to considering the $\color{red} {geometric}$ version of following:
Question: Since we could consider the ...
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2answers
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Elementary Question about Torsion Subgroups
Let $G$ be an abelian group which is killed by multiplication with the integer $n\geq 1$.
Let $n=a\cdot b$ with $a,b \geq 1$ and relatively prime.
Denote by $G[a]$ resp. $G[b]$ the $a$-resp. ...
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vote
1answer
228 views
Torsion subgroup
Prove that in a finitely generated abelian group $G$ the torsion subgroup is a direct summand (from Scott, Group Theory). Clearly, the torsion subgroup is normal because $G$ is abelian, so we have to ...
4
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2answers
421 views
A condition for a subgroup of a finitely generated free abelian group to have finite index
Let A be a free Abelian group of finite rank and B be a subgroup of A such that $A=B+pA$ for some prime number p, then how to prove $B$ is a subgroup of finite index in A? And if $A=B+pA$ holds for ...
