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MATHEMATICS
On Lockett pairs and Lockett conjecture for σ-local Fitting classes
E. D. Lantsetova P.M. Masherov Vitebsk State University
Abstract:
For each nonempty Fitting class F, Lockett defined the smallest Fitting class F∗ containing F such that (G×H)F∗=GF∗×HF∗ for all groups G and H and the Fitting class F∗ as the intersection of all nonempty Fitting classes X for which X∗=F∗. Lockett pair of nonempty Fitting classes F and H is an ordered pair (F,H) such that F∩H∗=(F∩H)∗. If F⊆H and F is a Lockett class, then F is said to satisfy Lockett conjecture in H. In the present paper, in the universe S of all finite soluble groups, the methods for constructing Lockett pairs are described for the case when F is a generalized local Fitting class, and, in particular, for F confirmed Lockett conjecture.
Keywords:
σ-local Fitting class, Lockett pair, Lockett conjecture.
Received: 03.02.2022
Citation:
E. D. Lantsetova, “On Lockett pairs and Lockett conjecture for σ-local Fitting classes”, PFMT, 2022, no. 2(51), 76–82
Linking options:
https://www.mathnet.ru/eng/pfmt847 https://www.mathnet.ru/eng/pfmt/y2022/i2/p76
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Abstract page: | 88 | Full-text PDF : | 38 | References: | 17 |
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