RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy Inst. Mat. i Mekh. UrO RAN: Year: Volume: Issue: Page: Find

 Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 4, Pages 155–166 (Mi timm1009)

On nonabelian composition factors of a finite group that is prime spectrum minimal

N. V. Maslovaab, D. O. Revincd

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
d Novosibirsk State University

Abstract: Suppose that $L$ is a finite group, $\pi(L)$ is the set of prime divisors of the order $|L|$, and $\mathfrak{Y}$ is the class of finite groups $G$ such that $\pi(G) \not = \pi(H)$ for any proper subgroup $H$ of $G$. Groups from the class $\mathfrak{Y}$ will be called prime spectrum minimal. Many but not all finite simple groups are prime spectrum minimal. For finite simple groups not from the class $\mathfrak{Y}$, the question whether they are isomorphic to nonabelian composition factors of groups from the class $\mathfrak{Y}$ is interesting. We describe some finite simple groups that are not isomorphic to nonabelian composition factors of groups from the class $\mathfrak{Y}$ and construct an example of a finite group from $\mathfrak{Y}$ that has as its composition factor a finite simple sporadic McLaughlin group $McL$ not from the class $\mathfrak{Y}$.

Keywords: finite group, prime spectrum, minimal group, maximal subgroup, composition factor.

Full text: PDF file (219 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 287, suppl. 1, 116–127

Bibliographic databases:

UDC: 512.542

Citation: N. V. Maslova, D. O. Revin, “On nonabelian composition factors of a finite group that is prime spectrum minimal”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 155–166; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 116–127

Citation in format AMSBIB
\Bibitem{MasRev13} \by N.~V.~Maslova, D.~O.~Revin \paper On nonabelian composition factors of a finite group that is prime spectrum minimal \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2013 \vol 19 \issue 4 \pages 155--166 \mathnet{http://mi.mathnet.ru/timm1009} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3364373} \elib{http://elibrary.ru/item.asp?id=20640508} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2014 \vol 287 \issue , suppl. 1 \pages 116--127 \crossref{https://doi.org/10.1134/S0081543814090119} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000345589100011} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84912049035} 

• http://mi.mathnet.ru/eng/timm1009
• http://mi.mathnet.ru/eng/timm/v19/i4/p155

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. V. Maslova, “Finite simple groups that are not spectrum critical”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 211–215
2. N. V. Maslova, “Finite groups with arithmetic restrictions on maximal subgroups”, Algebra and Logic, 54:1 (2015), 65–69
3. N. V. Maslova, “On the finite prime spectrum minimal groups”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 109–119
4. W. Guo, D. O. Revin, “Maximal and submaximal $\mathfrak X$-subgroups”, Algebra and Logic, 57:1 (2018), 9–28
•  Number of views: This page: 273 Full text: 66 References: 67 First page: 1