On the exponent of mutually permutable products of two abelian groups

Abstract

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in JOURNAL OF ALGEBRA [VOL 466, (15 November 2016)] DOI 10.1016/j.jalgebra.2016.05.027In this paper we obtain some bounds for the exponent of a finite group, and its derived subgroup, which is a mutually permutable product of two abelian subgroups. They improve the ones known for products of finite abelian groups, and they are used to derive some interesting structural properties of such products.The first author has been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. He has been also supported by a project from the National Natural Science Foundation of China (NSFC, No. 11271085) and a project of Natural Science Foundation of Guangdong Province (No. 2015A030313791).Ballester Bolinches, A.; Cossey, J.; Pedraza Aguilera, MC. (2016). On the exponent of mutually permutable products of two abelian groups. Journal of Algebra. 466:34-43. https://doi.org/10.1016/j.jalgebra.2016.05.027S344346