Algebra i logika
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



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i logika, 2003, Volume 42, Number 3, Pages 271–292 (Mi al30)  

This article is cited in 6 scientific papers (total in 6 papers)

Frobenius Groups Generated by Quadratic Elements

A. Kh. Zhurtov, V. D. Mazurova

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (252 kB) Citations (6)
References:
Abstract: An automorphism $a$ of a group $X$ is said to be quadratic if there exist integers $m=m(a)$ and $n=n(a)$ such that $x^{a^2}=x^n(x^m)^a= x^nx^{ma}$ for any $x\in X$. If $G$ is a Frobenius group then an element $g\in G$ is said to be quadratic if $g$ induces, by conjugation in the core of $G$, a quadratic automorphism. By definition, a group $H$ acts on a group $F$ freely if $f^h=f$ for $f\in F$ and $h\in H$ only with $f=1$ or $h=1$. It is proved that a Frobenius group generated by two quadratic elements is finite and its core is commutative. In particular, any Frobenius group generated by two elements of order at most 4 is finite. Also we argue that a Frobenius group with finitely generated soluble core is finite. The results mentioned are used to show that a group $G$ acting freely on an Abelian group is finite if it is generated by elements of order 3, and the order of a product of every two elements of order 3 in $G$ is finite.
Keywords: Frobenius group, quadratic automorphism, quadratic element.
Received: 23.10.2001
English version:
Algebra and Logic, 2003, Volume 42, Issue 3, Pages 153–164
DOI: https://doi.org/10.1023/A:1023932525056
Bibliographic databases:
UDC: 512.542
Language: Russian
Citation: A. Kh. Zhurtov, V. D. Mazurov, “Frobenius Groups Generated by Quadratic Elements”, Algebra Logika, 42:3 (2003), 271–292; Algebra and Logic, 42:3 (2003), 153–164
Citation in format AMSBIB
\Bibitem{ZhuMaz03}
\by A.~Kh.~Zhurtov, V.~D.~Mazurov
\paper Frobenius Groups Generated by Quadratic Elements
\jour Algebra Logika
\yr 2003
\vol 42
\issue 3
\pages 271--292
\mathnet{http://mi.mathnet.ru/al30}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2000843}
\zmath{https://zbmath.org/?q=an:1035.20034}
\elib{https://elibrary.ru/item.asp?id=8967710}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 3
\pages 153--164
\crossref{https://doi.org/10.1023/A:1023932525056}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645018656}
Linking options:
  • https://www.mathnet.ru/eng/al30
  • https://www.mathnet.ru/eng/al/v42/i3/p271
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
    Statistics & downloads:
    Abstract page:575
    Full-text PDF :143
    References:93
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024