Characterization of some finite simple groups by the set of orders of vanishing elements and order-Reference-Cited by-同舟云学术

Characterization of some finite simple groups by the set of orders of vanishing elements and order

Published:2021-11-23 Issue:11 Volume:73 Page:1443-1450
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

Askary S.

Abstract

UDC 512.5 <strong>Характеризацiя деяких скiнченних простих груп множиною порядкiв зникаючих елементiв та порядку</strong> Let be a finite group. We say that an element of is a vanishing element if there exists an irreducible complex character of such that . Ghasemabadi, Iranmanesh, Mavadatpour (2015), present the following conjecture: Let be a finite group and a finite nonabelian simple group such that and . Then . We answer in affirmative this conjecture for , where and either or is a prime number and , where and either or is prime.

Publisher

Institute of Mathematics National Academy of Sciences of Ukraine

Reference18 articles.

1. S. Asgary, N. Ahanjideh, Characterization of $P SL(3, q)$ by nse, Math. Rep., 19 (60), № 4, 425 – 438 (2017).

2. S. Asgary, N. Ahanjideh, nse characterization of some finite simple groups, Sci. Ann. Comput. Sci., 3 (2), 797 – 806 (2016).

3. G. Chen, Further reflections on Thompson’s conjecture, J. Algebra, 218, 276 – 285 (1999), https://doi.org/10.1006/jabr.1998.7839

4. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups, Clarendon Press, New York (1985).

5. G. Y. Chen, On Frobenius and 2-Frobenius group, J. Southwest China Normal Univ., 20, № 5, 485 – 487 (1995).