This article is cited in 11 papers

Characterization of the soluble one-generated totally saturated formations of finite groups

V. G. Safonov

Francisk Skorina Gomel State University

Abstract: We prove that the finite length condition for the lattice of $\tau$-closed totally saturated subformations of a $\tau$-closed totally saturated formation is equivalent to the finite length condition for this lattice, and it is also equivalent for the formation to be soluble and one-generated.

Keywords: formation of finite groups, totally saturated formation, lattice of formations, $\tau$-closed formation, one-generated formation.

UDC: 512.542

Received: 30.11.2005

 English version: Siberian Mathematical Journal, 2007, 48:1, 150–155

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