Centralizer-like Subgroups Associated with the $n$-Engel Words Inside of Direct Product Groups

Bridget Lee; Maggie Reardon; Faculty Mentor Dandrielle Lewis

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arXiv · 1911.03969

Centralizer-like Subgroups Associated with the $n$-Engel Words Inside of Direct Product Groups

Bridget Lee·Maggie Reardon·Faculty Mentor Dandrielle Lewis

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Abstract

This research provides a characterization of centralizer-like subgroups associated with the $n$-Engel word in a direct product of groups. Specifically, properties of the set of right $n$-Engel elements inside of direct products are explored. A proof is given to demonstrate the equivalence between the set of right $n$-Engel elements of a direct product of two groups and a direct product of the set of right $n$-Engel elements of each direct factor. This work was inspired by the study of centralizer-like subgroups in paper written by Luise-Charlotte Kappe and Patrick Ratchford. We present additional questions explored during this project, and we propose future research possibilities.

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BibTeX RIS

Bridget Lee, Maggie Reardon, Faculty Mentor Dandrielle Lewis. 2019-11-10. Centralizer-like Subgroups Associated with the $n$-Engel Words Inside of Direct Product Groups. https://arxiv.org/abs/1911.03969

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