Title : ( On the Exterior G-Center Subgroup of a Pair of Groups )
Authors: A. POURMIRZAEI , A. HOKMABADI , Saeed Kayvanfar ,
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Abstract
A group G is called capable if it is the group of inner automor- phisms of some group E. In 1996, Ellis introduced the exterior G-center subgroup, Z^ G (N), with the property that a pair (G;N) is capable if and only if Z^ G (N) = 1. In this paper we intend to describe this subgroup in terms of a free presentation of G. Also, we introduce a subgroup of Z(G;N), named the precise center of the pair (G;N), which is another criterion for characterizing capable pairs of groups.
Keywords
, Pair of Groups, Capability, Exterior G-Center
@inproceedings{paperid:1027720,
author = {A. POURMIRZAEI and A. HOKMABADI and Kayvanfar, Saeed},
title = {On the Exterior G-Center Subgroup of a Pair of Groups},
booktitle = {the 22nd Iranian Algebra seminar},
year = {2012},
location = {سبزوار, IRAN},
keywords = {Pair of Groups; Capability; Exterior G-Center},
}
%0 Conference Proceedings
%T On the Exterior G-Center Subgroup of a Pair of Groups
%A A. POURMIRZAEI
%A A. HOKMABADI
%A Kayvanfar, Saeed
%J the 22nd Iranian Algebra seminar
%D 2012
