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Sibirsk. Mat. Zh., 2009, Volume 50, Number 6, Pages 1319–1327 (Mi smj2051)  

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.

Full text: PDF file (334 kB)
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English version:
Siberian Mathematical Journal, 2009, 50:6, 1038–1044

Bibliographic databases:

UDC: 512.542
Received: 11.03.2008
Revised: 28.02.2009

Citation: E. N. Zalesskaya, N. N. Vorob'ev, “Lattices of partially local fitting classes”, Sibirsk. Mat. Zh., 50:6 (2009), 1319–1327; Siberian Math. J., 50:6 (2009), 1038–1044

Citation in format AMSBIB
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\by E.~N.~Zalesskaya, N.~N.~Vorob'ev
\paper Lattices of partially local fitting classes
\jour Sibirsk. Mat. Zh.
\yr 2009
\vol 50
\issue 6
\pages 1319--1327
\mathnet{http://mi.mathnet.ru/smj2051}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2603872}
\transl
\jour Siberian Math. J.
\yr 2009
\vol 50
\issue 6
\pages 1038--1044
\crossref{https://doi.org/10.1007/s11202-009-0114-4}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-74549201005}


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