Groups with Restrictions on Infinite Conjugacy Classes

Abstract. We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i) |NG(H) : H| < ∞ for every H ⋪ G, and (ii) |CG(x) : x | < ∞ for every x ⋪ G. We show that (i) and (ii) are equivalent in the classes of locally finite groups and locally nilpotent groups. In both cases, the groups satisfying these conditions are a special kind of cyclic extensions of Dedekind groups. We also study a variation of (i) and (ii), where the requirement of finiteness is replaced with a bound. In this setting, we extend our analysis to the classes of periodic locally graded groups and non-periodic groups. While the two conditions are still equivalent in the former case, in the latter the condition about normalizers is stronger than that about centralizers.

show abstract

Some finiteness conditions on normalizers or centralizers in groups

Fernández-Alcober

Legarreta

Tortora

et al. 2017

Communications in Algebra

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Groups with Restrictions on Infinite Conjugacy Classes

Cited by 1 publication

References 6 publications

Some finiteness conditions on normalizers or centralizers in groups

Some finiteness conditions on normalizers or centralizers in groups

Contact Info

Product

Resources

About