11th Algebra Seminar , 1999-10-27

Title : ( Some Results on the N_c-Capable Groups )

Authors: Saeed Kayvanfar ,

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Abstract Let { cal N}_c be the variety of nilpotent groups of class at most c (c geq 1) . We say that a group G is { cal N}_c -capable if G cong E/Z_c(E) , for some group E . In this talk it is shown that if G is an { cal N}_c -capable group and also G gamma_{c+1}(G) is of finite exponent, then the exponent of the i^{th} -center, Z_i(G) , for all 1 leq i leq c , divides the exponent of G gamma_{c+1}(G) . This generalizes a result of F.R.Beyl et al to the variety of nilpotent groups. Invoking this property, we shall establish a situation under which an { cal N}_c -perfect group may be { cal N}_c -capable. Using a corollary of P.Hall s type, it is shown that under which condition a group is not { cal N}_c -capable. Then some special class of groups which satisfy in the last condition will be presented. In fact, they are not { cal N}_c -capable.


Capable Groups
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author = {Kayvanfar, Saeed},
title = {Some Results on the N_c-Capable Groups},
booktitle = {11th Algebra Seminar},
year = {1999},
location = {اصفهان, IRAN},
keywords = {Capable Groups},


%0 Conference Proceedings
%T Some Results on the N_c-Capable Groups
%A Kayvanfar, Saeed
%J 11th Algebra Seminar
%D 1999