Abstract
ABSTRACT In this paper, among other results, we give some sufficient conditions for every non-abelian subgroup of a group to be isoclinic with the group itself. It is also seen that under certain conditions, two groups have same number of element centralizers implies they are isoclinic. We prove that if G is any group having 4, 5, 7 or 9 element centralizers and H is any non-abelian subgroup of G, then and or respectively. Furthermore, it is proved that if G is any group having element centralizers, then . Communicated by Mark Lewis
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