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| Paper IPM / M / 8011 |
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| Abstract: | |
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Let G be a group and let cent (G) denote the set of
centralizers of single elements of G. A group G is called
n−centralizer if |cent (G)|=n. In this paper, for a finite
group G, we give some interesting relations between |cent (G)|
and the maximum number of the pairwise non-commuting elements in
G. Also we characterize all n−centralizer finite groups for
n=7 and 8. Using these results we prove that there is no finite
group G with the property that |cent (G)|=|cent([(G)/(Z(G))])|=8, where Z(G) denotes the centre of G. This
latter result answers positively a conjecture posed by A. R.
Ashrafi.
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