The authors classify finite groups in which the order of each centralizer of a noncentral element has at most two prime factors. There are several types of such solvable groups and the nonsolvable ones are SL(2,5) and PSL(2,5) . The result is an analogue of similar results that were proved recently for groups with arithmetical conditions on the sizes of the conjugacy classes of the noncentral elements.
Groups with small centralizers of noncentral elements / M. Bianchi, O. Manz. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A. - ISSN 0392-4033. - 4:3(1990), pp. 365-370.
Groups with small centralizers of noncentral elements
M. Bianchi;
1990
Abstract
The authors classify finite groups in which the order of each centralizer of a noncentral element has at most two prime factors. There are several types of such solvable groups and the nonsolvable ones are SL(2,5) and PSL(2,5) . The result is an analogue of similar results that were proved recently for groups with arithmetical conditions on the sizes of the conjugacy classes of the noncentral elements.
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