Tagged: fourth isomorphism theorem
Problem 557
Let $N$ be a normal subgroup of a group $G$.
Suppose that $G/N$ is an infinite cyclic group.
Then prove that for each positive integer $n$, there exists a normal subgroup $H$ of $G$ of index $n$.
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Ring theory
by
Yu
· Published 11/24/2016
· Last modified 08/11/2017
Problem 197
Let $R$ be a ring with unit $1\neq 0$.
Prove that if $M$ is an ideal of $R$ such that $R/M$ is a field, then $M$ is a maximal ideal of $R$.
(Do not assume that the ring $R$ is commutative.)
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Group Theory
by
Yu
· Published 09/26/2016
· Last modified 07/29/2017
Problem 122
Let $G$ be a finite group. Then show that $G$ has a composition series.
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