finite groups have even more centralizers

Authors

s. m. jafarian amri

m. amiri

h. madadi

h. rostami

abstract

for a finite group $g$‎, ‎let $cent(g)$ denote the set of centralizers of single elements of $g$‎. ‎in this note we prove that if $|g|leq frac{3}{2}|cent(g)|$ and $g$ is 2-nilpotent‎, ‎then $gcong s_3‎, ‎d_{10}$ or $s_3times s_3$‎. ‎this result gives a partial and positive answer to a conjecture raised by a‎. ‎r‎. ‎ashrafi [on finite groups with a given number of centralizers‎, ‎algebra‎ ‎colloq. 7 (2000)‎, ‎no‎. ‎2‎, ‎139--146]‎.

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Finite groups have even more centralizers

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Journal title:
bulletin of the iranian mathematical society

Publisher: iranian mathematical society (ims)

ISSN 1017-060X

volume 41

issue 6 2015

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