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Mat. Zametki, 2008, Volume 83, Issue 4, Pages 520–527 (Mi mz4572)  

Critical Non-Singly-Generated Totally Canonical Fitting Classes of Finite Groups

V. E. Egorova

Moscow State Pedagogical University

Abstract: Let $\mathfrak I$ be the class of all finite simple groups and $f\colon\mathfrak I\to\{Fitting classes of groups\}$. The Fitting class $\mathfrak F=KR(f)=(G:O^{A,A'}(G)\in f(A) for any A \in K(G))$ is referred to as a canonical Fitting class with satellite $f$. A non-singly-generated totally canonical Fitting class $\mathfrak F$ is said to be critical non-singly-generated if all proper totally canonical Fitting subclasses in $\mathfrak F$ are singly generated. In the paper, a complete description of the structure of the critical non-singly-generated totally canonical Fitting classes of finite groups is obtained.

Keywords: finite simple group, Fitting class, Fitting formation, satellite, singly generated Fitting class, local formation of finite groups

DOI: https://doi.org/10.4213/mzm4572

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English version:
Mathematical Notes, 2008, 83:4, 478–484

Bibliographic databases:

UDC: 512.542
Received: 29.12.2006
Revised: 26.06.2007

Citation: V. E. Egorova, “Critical Non-Singly-Generated Totally Canonical Fitting Classes of Finite Groups”, Mat. Zametki, 83:4 (2008), 520–527; Math. Notes, 83:4 (2008), 478–484

Citation in format AMSBIB
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