Let p be a prime and G a pro-p group of finite rank that admits a faithful, self-similar action on the p-ary rooted tree. We prove that if the set {g∈G∣gpn=1} is a nontrivial subgroup for some n, then G is a finite p-group with exponent at most pn. This applies, in particular, to power abelian p-groups.
Alex Carrazedo Dantas; Emerson de Melo. Exponent of self-similar finite $p$-groups. Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1369-1375. doi: 10.4171/ggd/754
@article{10_4171_ggd_754,
author = {Alex Carrazedo Dantas and Emerson de Melo},
title = {Exponent of self-similar finite $p$-groups},
journal = {Groups, geometry, and dynamics},
pages = {1369--1375},
year = {2024},
volume = {18},
number = {4},
doi = {10.4171/ggd/754},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/754/}
}
TY - JOUR
AU - Alex Carrazedo Dantas
AU - Emerson de Melo
TI - Exponent of self-similar finite $p$-groups
JO - Groups, geometry, and dynamics
PY - 2024
SP - 1369
EP - 1375
VL - 18
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/754/
DO - 10.4171/ggd/754
ID - 10_4171_ggd_754
ER -
%0 Journal Article
%A Alex Carrazedo Dantas
%A Emerson de Melo
%T Exponent of self-similar finite $p$-groups
%J Groups, geometry, and dynamics
%D 2024
%P 1369-1375
%V 18
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/754/
%R 10.4171/ggd/754
%F 10_4171_ggd_754
