A note on semidirect products and nonabelian tensor products of groups
Algebra and discrete mathematics, no. 3 (2009), pp. 77-84
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Let $G$ and $H$ be groups which act compatibly on one another. In [2] and [8] it is considered a group construction $\eta(G,H)$ which is related to the nonabelian tensor product $G\otimes H$. In this note we study embedding questions of certain semidirect products $A\rtimes H$ into $\eta(A, H)$, for finite abelian $H$-groups $A$. As a consequence of our results we obtain that complete Frobenius groups and affine groups over finite fields are embedded into $\eta(A, H)$ for convenient groups $A$ and $H$. Further, on considering finite metabelian groups $G$ in which the derived subgroup has order coprime with its index we establish the order of the nonabelian tensor square of $G$.
@article{ADM_2009_3_a7,
author = {Irene N. Nakaoka and Nora{\'\i} R. Rocco},
title = {A note on semidirect products and nonabelian tensor products of groups},
journal = {Algebra and discrete mathematics},
pages = {77--84},
publisher = {mathdoc},
number = {3},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADM_2009_3_a7/}
}
Irene N. Nakaoka; Noraí R. Rocco. A note on semidirect products and nonabelian tensor products of groups. Algebra and discrete mathematics, no. 3 (2009), pp. 77-84. http://geodesic.mathdoc.fr/item/ADM_2009_3_a7/