Asian-European Journal of Mathematics, Volume (4), No (2), Year (2011-1) , Pages (271-282)

Title : ( SOME CONSIDERATIONS ON THE NONABELIAN TENSOR SQUARE OF CRYSTALLOGRAPHIC GROUPS )

Authors: Ahmad Erfanian , Francesco Russo , N. H. Sarmin ,

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The nonabelian tensor square G ⊗ G of a polycyclic group G is a polycyclic group and its structure arouses interest in many contexts. The same assertion is still true for wider classes of solvable groups. This motivated us to work on two levels in the present paper: on a hand, we investigate the growth of the Hirsch length of G⊗G by looking at that of G, on another hand, we study the nonabelian tensor product of pro–p–groups of finite coclass, which are a remarkable class of solvable groups without center, and then we do considerations on their Hirsch length. Among other results, restrictions on the Schur multiplier will be discussed.

Keywords

, Schur multiplier; polycyclic groups; pro–p–groups of finite co, class; Bieberbach
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@article{paperid:1026358,
author = {Erfanian, Ahmad and Francesco Russo and N. H. Sarmin},
title = {SOME CONSIDERATIONS ON THE NONABELIAN TENSOR SQUARE OF CRYSTALLOGRAPHIC GROUPS},
journal = {Asian-European Journal of Mathematics},
year = {2011},
volume = {4},
number = {2},
month = {January},
issn = {1793-5571},
pages = {271--282},
numpages = {11},
keywords = {Schur multiplier; polycyclic groups; pro–p–groups of finite co- class; Bieberbach groups.},
}

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%0 Journal Article
%T SOME CONSIDERATIONS ON THE NONABELIAN TENSOR SQUARE OF CRYSTALLOGRAPHIC GROUPS
%A Erfanian, Ahmad
%A Francesco Russo
%A N. H. Sarmin
%J Asian-European Journal of Mathematics
%@ 1793-5571
%D 2011

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