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There is a definition which help us to understand the semi-direct product well:

Let $K$ be a subgroup of a group $G$. Then a subgroup $Q\leq G$ is a complement of $K$ in $G$ if $K\cap Q=1$ and $KQ=G$.

Habitually, whenever I see the form $KQ=G$, I think of one of the subgroups $K$ or $Q$ are at least normal in group. But in the definition above J.J.Rotman quoted that $K$ is not necessarily normal in $G$ and moreover he didn't say anything about normality for $Q$ as well.

May I ask you to present me an example, having two subgroups not normal in $G$, and yet $G=KQ$? And if I misunderstand about above, please tell me. Thanks.

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Take $G = A_{5}$,$K = A_{4}$ (say the subgroup of $A_{5}$ fixing $5$) and $Q$ to be a Sylow $5$-subgroup of $A_{5}.$

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    As for the second question, it is a matter of language and definition. My interpretation would be that I would expect them to mean the same thing, but I have not looked at the link2012-09-16
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This is sometimes called a(n internal) Zappa-Szép product. There are examples at the Wikipedia article.