Asian Journal of Mathematics and Computer Research

ON SOLVABILITY OF CERTAIN IRREDUCIBLE LINEAR GROUPS

ALEKSEY YADCHENKO *

Institute of Mathematics of the National Academy of Sciences of the Republic of Belarus, 32a Kirova Street, 246050 Gomel, Republic of Belarus.

*Author to whom correspondence should be addressed.

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Abstract

The paper particularly shows that a π-solvable irreducible linear group G of the power of n less than 2|H|, whose π-Hall TI-subgroup H is not normal in G, is solvable, probably with the exception of the case n = 2(|H| − 1). In this case we have (C_G(H))_π′/Z(G) ≅ PSL(2, 5).

Keywords: A finite groups, a normal subgroups, a characters of groups, cosimple automorphisms of groups

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