Конечные группы с холловыми $\pi$-подгруппами

Denote by {\nu_{p}(G)} the number of Sylow p-subgroups of G. It is not difficult to see that {\nu_{p}(H)\leqslant\nu_{p}(G)} for {H\leqslant G}, however {\nu_{p}(H)} does not divide {\nu_{p}(G)} in general. In this paper we reduce the question whether {\nu_{p}(H)} divides {\nu_{p}(G)} for every {H\leqslant G} to almost simple groups. This result substantially generalizes the previous result by G. Navarro and also provides an alternative proof of Navarro’s theorem.

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Конечные группы с холловыми $\pi$-подгруппами

Cited by 5 publications

References 19 publications

Groups of Induced Automorphisms and Their Application to Studying the Existence Problem for Hall Subgroups

Groups of Induced Automorphisms and Their Application to Studying the Existence Problem for Hall Subgroups

The Structure of Groups Possessing Carter Subgroups of Odd Order

Number of Sylow subgroups in finite groups

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