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Abstract
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In this paper we study the coprime graph of a group G. The coprime graph
of a group G, denoted by \Gamma_G, is a graph whose vertices are elements of G
and two distinct vertices x and y are adjacent if and only if (|x|,|y|) = 1.
In this paper, we show that if G and H are two nilpotent groups of order n
then \Gamma_G=Gamma_H
Also we classify maximal independent sets in groups with
at most three prime factors.
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