On Burnside's $p^\alpha q^\beta$ theorem

A. V. Korlyukov

M. V. Lomonosov Moscow State University

Abstract: We study finite groups whose conjugate element classes have dimensions of the form $p^\alpha q^\beta$. We prove that the factors of the composition series of any such group either are cyclic or are isomorphic to one of the groups PSL(2, 4), PSL(2, 8).

UDC: 519.4

Received: 11.06.1974

 English version: Mathematical Notes, 1975, 17:2, 161–164

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