Algebra Colloquium, ( ISI ), Volume (4), No (1), Year (1997-1) , Pages (1-11)

Title : ( A New Notion Derived from Varieties of Group )

Authors: Mohammad Reza Rajabzadeh Moghaddam , Saeed Kayvanfar ,

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Let cal V be a variety of groups defined by the set of laws V , it is shown that every group G possesses a uniquely determined subgroup (V^*)^*(G) of the marginal subgroup V^*(G) , which is minimal subject to being the image in G of the marginal subgroup of some cal V -marginal extension of G . (V^*)^*(G) is characteristic and is also the smallest subgroup of V^*(G) whose factor-group is cal V -capable. The Stallings sequence, and the Ganea sequence up to the left term, are also generalized to an arbitrary variety of groups. Finally if { cal N}_c is the variety of nilpotent groups of class at most c (c geq 1) , and G is an { cal N}_c -capable group and also G /gamma_{c+1}(G) is of finite exponent, then it is shown that the exponent of the i^{th} -centre , Z_i(G) , for all 1 leq i leq c , divides the exponent of G gamma_{c+1}(G) .


, Baer-invariant, variety, cal V -capable.
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author = {Rajabzadeh Moghaddam, Mohammad Reza and Kayvanfar, Saeed},
title = {A New Notion Derived from Varieties of Group},
journal = {Algebra Colloquium},
year = {1997},
volume = {4},
number = {1},
month = {January},
issn = {1005-3867},
pages = {1--11},
numpages = {10},
keywords = {Baer-invariant;variety; cal V -capable.},


%0 Journal Article
%T A New Notion Derived from Varieties of Group
%A Rajabzadeh Moghaddam, Mohammad Reza
%A Kayvanfar, Saeed
%J Algebra Colloquium
%@ 1005-3867
%D 1997