Abstract
We study finite groups whose conjugate element classes have dimensions of the form pαqβ. 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).
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Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 277–284, February, 1975.
The author is deeply grateful to A. I. Kostrikin for posing the problem and for valuable advice.
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Korlyukov, A.V. On Burnside's pαqβ theorem. Mathematical Notes of the Academy of Sciences of the USSR 17, 161–164 (1975). https://doi.org/10.1007/BF01161873
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DOI: https://doi.org/10.1007/BF01161873