L.S. Kazarin. On products of $\pi$-solvable finite groups ... P. 109-120

In this paper, we study finite groups having a triple factorization $G=AB=AC=BC$, where the factors $A$, $B$, and $C$ are $\pi$-solvable subgroups of the group $G$ for some set $\pi$ of primes. This problem seems to have been first formulated by A.F. Vasil'ev and A.K. Furs in 2021 at the conference dedicated to the 90th anniversary of the birth of A.I. Starostin.

Keywords: finite group, subgroup, character, representation, factorization

Received April 15, 2023

Revised August 16, 2023

Accepted August 28, 2023

Funding Agency: This work was supported by Yaroslavl State University (program no. VIP-008).

Lev Sergeevich Kazarin, Dr. Phys.-Math. Sci., Prof., Yaroslavl P. Demidov State University, Yaroslavl, 150001 Russia, e-mail: lsk46@mail.ru

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Cite this article as: L.S. Kazarin. On products of $\pi$-solvable finite groups. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, vol. 29, no. 4, pp. 109–120.