This article is cited in 1 paper

Lattices of partially local fitting classes

E. N. Zalesskaya, N. N. Vorob'ev

Vitebsk State University, Vitebsk, Belarus

Abstract: This article deals only with finite groups. We prove the surjectivity of the mapping from the lattice of all normal Fitting classes into the lattice of the Lockett section generated by the Fitting classes that are not Lockett classes. Moreover, we find a sufficient surjectivity condition for the mapping of the lattice of the Lockett section generated by arbitrary Fitting classes into the lattice of the Lockett section generated by $\omega$-local Fitting classes. This confirms Lockett's conjecture for the $\omega$-local Fitting classes of a given characteristic.

Keywords: lattice of Fitting classes, $\omega$-local Fitting class, Lockett class, Lockett section, Lockett's conjecture.

UDC: 512.542

Received: 11.03.2008
Revised: 28.02.2009

 English version: Siberian Mathematical Journal, 2009, 50:6, 1038–1044

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