نظریه گروه ها-International Journal of Group Theory, Volume (1), No (4), Year (2012-1) , Pages (1-7)

Title : ( On the groups satisfying the converse of Schur s theorem )

Authors: azam kaheni , Rasoul Hatamian , Saeed Kayvanfar ,

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Abstract

A famous theorem of Schur states that for a group G niteness of G=Z(G) implies the niteness of G0: The converse of Schur s theorem is an interesting problem which has been considered by some authors. Recently, Podoski and Szegedy proved the truth of the converse of Schur s theorem for capable groups. They also established an explicit bound for the index of the center of such groups. This paper is devoted to determine some families of groups among non-capable groups which satisfy the converse of Schur s theorem and at the same time admit the Podoski and Szegedy s bound as the upper bound for the index of their centers.

Keywords

, Capable group, n-isoclinism, Extra special p-group, Schur s theorem.
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@article{paperid:1034189,
author = {Kaheni, Azam and Hatamian, Rasoul and Kayvanfar, Saeed},
title = {On the groups satisfying the converse of Schur s theorem},
journal = {نظریه گروه ها-International Journal of Group Theory},
year = {2012},
volume = {1},
number = {4},
month = {January},
issn = {2251-7650},
pages = {1--7},
numpages = {6},
keywords = {Capable group; n-isoclinism; Extra special p-group; Schur s theorem.},
}

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%0 Journal Article
%T On the groups satisfying the converse of Schur s theorem
%A Kaheni, Azam
%A Hatamian, Rasoul
%A Kayvanfar, Saeed
%J نظریه گروه ها-International Journal of Group Theory
%@ 2251-7650
%D 2012

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