Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I would like to ask if $G$ is a semidirect product of a normal subgroup $N$ by a subgroup $K$.

Can we consider $N\wedge G$ as a subgroup of $G\wedge G$? In fact, is the following sequence exact $0\rightarrow N\wedge G\rightarrow G\wedge G \rightarrow G/N\wedge G/N \rightarrow 0$?


share|cite|improve this question
You will have to explain your question and cryptic notation for anyone to make progress on this. – rschwieb Aug 22 '12 at 16:05
Have you looked at this yet? – Alexander Gruber Aug 23 '12 at 5:44
Have you also tried using the fact that semidirect products are defined by extensions which split? – Ronnie Brown Aug 23 '12 at 9:48
For a moment I thought the symbol $\,\wedge\,$ within this context could mean intersection, but $\,G\wedge G\,$ would be boringly trivial, so...?? – DonAntonio Aug 25 '12 at 3:52

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.