Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Khukhro, Evgenii I. / Kramer, Linus

6 Issues per year


IMPACT FACTOR 2016: 0.457
5-year IMPACT FACTOR: 0.521

CiteScore 2016: 0.53

SCImago Journal Rank (SJR) 2016: 0.673
Source Normalized Impact per Paper (SNIP) 2016: 1.049

Mathematical Citation Quotient (MCQ) 2016: 0.43

Online
ISSN
1435-4446
See all formats and pricing
More options …
Volume 18, Issue 5 (Sep 2015)

Issues

On the structure of finite groups isospectral to finite simple groups

Mariya A. Grechkoseeva
  • Sobolev Institute of Mathematics, Ac. Koptyuga 4, Novosibirsk, 630090, Russia; and Novosibirsk State University, Pirogova 2, Novosibirsk, 630090, Russia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Andrey V. Vasil'ev
  • Sobolev Institute of Mathematics, Ac. Koptyuga 4, Novosibirsk, 630090, Russia; and Novosibirsk State University, Pirogova 2, Novosibirsk, 630090, Russia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-06-04 | DOI: https://doi.org/10.1515/jgth-2015-0019

Abstract

Finite groups are said to be isospectral if they have the same sets of element orders. A finite nonabelian simple group L is said to be almost recognizable by spectrum if every finite group isospectral to L is an almost simple group with socle isomorphic to L. It is known that all finite simple sporadic, alternating and exceptional groups of Lie type, except J2, A6, A10 and 3D4(2), are almost recognizable by spectrum. The present paper is the final step in the proof of the following conjecture due to V. D. Mazurov: there exists a positive integer d0 such that every finite simple classical group of dimension larger than d0 is almost recognizable by spectrum. Namely, we prove that a nonabelian composition factor of a finite group isospectral to a finite simple symplectic or orthogonal group L of dimension at least 10, is either isomorphic to L or not a group of Lie type in the same characteristic as L, and combining this result with earlier work, we deduce that Mazurov's conjecture holds with d0 = 60.

About the article

Received: 2014-12-08

Revised: 2015-04-21

Published Online: 2015-06-04

Published in Print: 2015-09-01


Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 13-01-00505


Citation Information: Journal of Group Theory, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2015-0019.

Export Citation

© 2015 by De Gruyter. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Yu. V. Lytkin
Siberian Mathematical Journal, 2017, Volume 58, Number 4, Page 633
[2]
M. A. Grechkoseeva
Siberian Mathematical Journal, 2016, Volume 57, Number 4, Page 582
[3]
A. V. Vasil’ev and M. A. Grechkoseeva
Siberian Mathematical Journal, 2015, Volume 56, Number 6, Page 1009
[4]
Mariya A. Grechkoseeva and Mariya A. Zvezdina
Journal of Algebra and Its Applications, 2016, Volume 15, Number 09, Page 1650168

Comments (0)

Please log in or register to comment.
Log in