ScienceAsia, ( ISI ), Volume (38), No (2), Year (2012-6) , Pages (201-206)

Title : ( Relative non nil n-graph of finite groups )

Authors: Ahmad Erfanian , Behnaz Tolue Haghighi ,

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ABSTRACT: Suppose G is not a nilpotent group of class at most n (a non nil-n group). Consider a subgroup H of G. In this paper, we introduce the relative non nil-n graph (n) H;G of a finite group G. It is a graph with vertex set GnC(n) G(H) and two distinct vertices x and y are adjacent if at least one of them belongs toH and [x; y] = 2 Zn 1(G), where the subgroup C(n) G(H) contains g 2 G such that [g; h] 2 Zn 1(G) for all h 2 H. We present some general information about the graph. Moreover, we define the probability which shows how close a group is to being a nil-n group. It is proved that two n-isoclinic groups which are not nil-n groups have isomorphic graphs under special conditions.

Keywords

, nilpotent groups, nth nilpotency
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@article{paperid:1033027,
author = {Erfanian, Ahmad and Tolue Haghighi, Behnaz},
title = {Relative non nil n-graph of finite groups},
journal = {ScienceAsia},
year = {2012},
volume = {38},
number = {2},
month = {June},
issn = {1513-1874},
pages = {201--206},
numpages = {5},
keywords = {nilpotent groups; nth nilpotency degree},
}

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%0 Journal Article
%T Relative non nil n-graph of finite groups
%A Erfanian, Ahmad
%A Tolue Haghighi, Behnaz
%J ScienceAsia
%@ 1513-1874
%D 2012

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