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MATHEMATICS

On minimal $\sigma$-local non-$\mathfrak{H}$-formations of finite groups

I. N. Safonova

Belarusian State University, Minsk

Abstract: The critical $\sigma$-local formations of finite groups are studied, where $\sigma$ is some partition of the set of all primes $\mathbb{P}$. A criterion is obtained for critical $\sigma$-local formations. A description of critical $\sigma$-local formations is given for formations of all $\Pi$-groups, all $\sigma$-soluble $\Pi$-groups, where $\varnothing\ne\Pi\subseteq\sigma$, and a description of minimal $\sigma$-local non-$\sigma$-soluble formations of finite groups is obtained.

Keywords: finite group, formation $\sigma$-function, $\sigma$-local formation, local formation, critical $\sigma$-local formation, $\sigma$-soluble group.

UDC: 512.542

Received: 10.11.2020