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Mat. Zametki, 2013, Volume 94, Issue 3, Pages 455–472 (Mi mz8836)  

This article is cited in 1 scientific paper (total in 1 paper)

Criteria for the $p$-Solvability and $p$-Supersolvability of Finite Groups

Yufeng Liua, Guo Wenbinb, V. A. Kovalevac, A. N. Skibac

a Shandong Institute of Business and Technology
b University of Science and Technology of China
c Francisk Skorina Gomel State University

Abstract: Let $A$$K$, and $H$ be subgroups of a group $G$ and $K\leqslant H$. Then we say that $A$ covers the pair $(K,H)$ if $AH=AK$ and avoids the pair $(K,H)$ if $A\cap H=A\cap K$. A pair $(K,H)$ in $G$ is said to be maximal if $K$ is a maximal subgroup of $H$. In the present paper, we study finite groups in which some subgroups cover or avoid distinguished systems of maximal pairs of these groups. In particular, generalizations of a series of known results on (partial) $CAP$-subgroups are obtained.

Keywords: solvable group, supersolvable group, maximal pair, weakly $CAP_{p}$-subgroup, weakly $CAP$-subgroup, (conditional) cover-avoiding property of subgroups, (partial) $CAP$-subgroup.

DOI: https://doi.org/10.4213/mzm8836

Full text: PDF file (517 kB)
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English version:
Mathematical Notes, 2013, 94:3, 426–439

Bibliographic databases:

UDC: 512.542
Received: 22.02.2010
Revised: 14.01.2013

Citation: Yufeng Liu, Guo Wenbin, V. A. Kovaleva, A. N. Skiba, “Criteria for the $p$-Solvability and $p$-Supersolvability of Finite Groups”, Mat. Zametki, 94:3 (2013), 455–472; Math. Notes, 94:3 (2013), 426–439

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. V. A. Kovaleva, “Konechnye gruppy s zadannymi obobschenno maksimalnymi podgruppami (obzor). II. Ot maksimalnykh tsepei k maksimalnym param”, PFMT, 2017, no. 2(31), 55–65  mathnet
  • Математические заметки Mathematical Notes
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