Journal of Algebra, ( ISI ), Volume (1), No (127), Year (2001-1) , Pages (126-138)

#### Title : the category pme (g,v) and generalized covering groups ( The Category PME(G,V) and Generalized Covering Group )

Authors: Saeed Kayvanfar ,

Citation: BibTeX | EndNote

#### Abstract

The properties of covering and universality between the central extensions and also the structure of a covering group of perfect groups have been generalized by S.Kayvanfar and M.R.R.Moghaddam (Indag. Mathem., N.S, 8(4), 1997, 537-542) to the variety of groups defined by a set of outer commutator words. In this paper we generalize the above results to any variety of groups. Then we introduce the category ${\\cal PME}(G,{\\cal V})$ and using the above generalization, show that if $G$ is $\\cal V$-perfect then there exists a universal object in this category and its structure will be determined. Finally it is shown that any two $\\cal V$-covering groups of a $\\cal V$-perfect group are isomorphic and the structure of the unique generalized covering group of an arbitrary $\\cal V$-perfect group is introduced.

#### Keywords

, covering group , perfect group , variety of groups, category
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@article{paperid:201193,
author = {Kayvanfar, Saeed},
title = {the category pme (g,v) and generalized covering groups},
journal = {Journal of Algebra},
year = {2001},
volume = {1},
number = {127},
month = {January},
issn = {0021-8693},
pages = {126--138},
numpages = {12},
keywords = {covering group - perfect group - variety of groups- category},
}