PreprintCC BY 4.0arXiv
The R∞-nilpotency degree of some lollipop GBS groups
Abstract
We say that a group G has the R∞ property if the number R(φ) of twisted conjugacy classes is infinite for any automorphism φ of G. The R∞-nilpotency degree is the least integer c such that G/γc+1(G) has property R∞; in case this integer does not exist, we say that G has infinite R∞-nilpotency degree. In this paper, we determine the R∞-nilpotency degree of some lollipop GBS groups by using different approaches, such as Sylow subgroups, normal forms and presentation of nilpotent quotients, and diagrams of exact sequences. We also compute the R∞-nilpotency degree of all 2-generated lollipop GBS groups and of all GBS groups whose associated graph is a tree.
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BibTeX
@misc{sgobbi2026rnilpotency,
title = {{The $R_\infty$-nilpotency degree of some lollipop GBS groups}},
author = {Wagner Sgobbi and Dalton Couto Silva and Daniel Vendrúscolo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14204},
eprint = {2610.14204},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14204},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The R_∞-nilpotency degree of some lollipop GBS groups
AU - Wagner Sgobbi
AU - Dalton Couto Silva
AU - Daniel Vendrúscolo
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14204
UR - https://arxiv.org/abs/2610.14204
AB - We say that a group G has the R_∞ property if the number R(φ) of twisted conjugacy classes is infinite for any automorphism φ of G. The R_∞-nilpotency degree is the least integer c such that G/γ_c+1(G) has property R_∞; in case this integer does not exist, we say that G has infinite R_∞-nilpotency degree. In this paper, we determine the R_∞-nilpotency degree of some lollipop GBS groups by using different approaches, such as Sylow subgroups, normal forms and presentation of nilpotent quotients, and diagrams of exact sequences. We also compute the R_∞-nilpotency degree of all 2-generated lollipop GBS groups and of all GBS groups whose associated graph is a tree.
ER -