Geodesic
On Burnside's $p^\alpha q^\beta$ theorem
Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 277-283.

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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). 
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     author = {A. V. Korlyukov},
     title = {On {Burnside's} $p^\alpha q^\beta$ theorem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {277--283},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a9/}
}
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A. V. Korlyukov. On Burnside's $p^\alpha q^\beta$ theorem. Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 277-283. http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a9/