Groups of prime generalized exponent-Reference-Cited by-同舟云学术

Groups of prime generalized exponent

Published:2017-11 Issue:07 Volume:27 Page:849-862
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Abdollahi A.¹²,Daoud B.³,Farrokhi D. G. M.⁴,Guerboussa Y.⁵

Affiliation:

1. Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran

2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

3. Department of Mathematics, Laboratory of Fundamental and Numerical Mathematics, Ferhat Abbas University, Setif 1, Algeria

4. Mathematical Science Research Unit, College of Liberal Arts, Muroran Institute of Technology, 27-1, Mizumoto, Muroran 050-8585, Hokkaido, Japan

5. Department of Mathematics, University Kasdi Merbah Ouargla, Ouargla, Algeria

Abstract

A group [Formula: see text] satisfies a positive generalized identity of degree [Formula: see text] if there exist elements [Formula: see text] such that [Formula: see text] for all [Formula: see text]. The minimum degree of such an identity is called the generalized exponent of [Formula: see text]. Among other things, we prove that every finitely generated solvable group satisfying a positive generalized identity of prime degree is a finite [Formula: see text]-group. Consequently, we show that every finite group with a positive generalized identity of degree [Formula: see text] is a 5-group of exponent dividing 25.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196717500400

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