Mathematics – Group Theory
Scientific paper
2009-03-29
Mathematics
Group Theory
21 pages, final version to appear in Central European J. Math
Scientific paper
We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups $(H, G, \alpha, \beta)$ is deformed using a combinatorial datum $(\sigma, v, r)$ consisting of an automorphism $\sigma$ of $H$, a permutation $v$ of the set $G$ and a transition map $r: G\to H$ in order to obtain a new matched pair $\bigl(H, (G,*), \alpha', \beta' \bigl)$ such that there exist an $\sigma$-invariant isomorphism of groups $H {}_{\alpha} \bowtie_{\beta} G \cong H {}_{\alpha'} \bowtie_{\beta'} (G,*)$. Moreover, if we fix the group $H$ and the automorphism $\sigma \in \Aut(H)$ then any $\sigma$-invariant isomorphism $H {}_{\alpha} \bowtie_{\beta} G \cong H {}_{\alpha'} \bowtie_{\beta'} G'$ between two arbitrary bicrossed product of groups is obtained in a unique way by the above deformation method. As applications two Schreier type classification theorems for bicrossed product of groups are given.
Agore Ana-Loredana
Militaru Gigel
No associations
LandOfFree
Schreier type theorems for bicrossed products does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Schreier type theorems for bicrossed products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Schreier type theorems for bicrossed products will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-202475