Question
Suppose that $H$ is a normal subgroup of $G$. If $|H|=4$ and $g H$ has order 3 in $G / H$, find a subgroup of order 12 in $G$.
Step 1
Step 1: Since \( H \) is a normal subgroup of \( G \) with \( |H| = 4 \), we know that \( H \) is a subgroup of \( G \) and that the quotient group \( G/H \) is well-defined. Show more…
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Let $G$ be an abelian group. If $H=\left\{x \in G: x=x^{-1}\right\}$, that is, $H$ consists of all the elements of $G$ which are their own inverses, prove that $H$ is a subgroup of $G$.
SUBGROUPS
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