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On the solvability and factorization of some π-solvable irreducible linear groups of primary degree. Part II

Abstract

The article is the second in a series of papers where for a set $\pi$ of odd primes $\pi$-solvable finite irreducible complex linear groups of degree $2|H|+1$ whose Hall $\pi$-subgroups are $TI$-subgroups and are not normal in groups. The goal of this series is to prove the solvability and determine the factorization of such groups. The proof of the theorem is continued. Further properties of the minimal counterexample to the theorem are established.

About the Author

A. A. Yadchenko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus


References

1. Ядченко А. А. О разрешимости и факторизации некоторых π-разрешимых неприводимых линейных групп примарной степени. Часть I // Тр. Ин-та математики. 2022. Т. 30, № 1–2. С. 84–98.

2. Gorenstein D. Finite groups. New York: Harper and Row, 1968.

3. Isaacs I. M. Character theory of finite groups. New York: Academic Press, 1976.

4. Dixon J. The structure of linear groups. L.: Butler and Tanner Ltd., 1971.

5. Ядченко А. А., Романовский А. В. К проблеме Айзекса о конечных p -разрешимых линейных группах // Матем. заметки. 2001. Т. 69, Вып. 1. С. 144–152.

6. Ядченко А. А. О π-разрешимых неприводимых линейных группах с холловой TI подгруппой нечетного порядка I // Тр. Ин-та математики. 2008. Т. 16, № 2. С. 118–130.


Review

For citations:


Yadchenko A.A. On the solvability and factorization of some π-solvable irreducible linear groups of primary degree. Part II. Trudy Instituta matematiki. 2023;31(1):88-100. (In Russ.)

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ISSN 1812-5093 (Print)