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Profinite groups with many elements of bounded order

Authors
  • Abdollahi, Alireza
  • Malekan, Meisam Soleimani
Type
Preprint
Publication Date
Dec 27, 2020
Submission Date
Dec 27, 2020
Source
University of Michigan Library Repository
License
Green
External links

Abstract

L\'evai and Pyber proposed the following as a conjecture: Let $G$ be a profinite group such that the set of solutions of the equation $x^n=1$ has positive Haar measure. Then $G$ has an open subgroup $H$ and an element $t$ such that all elements of the coset $tH$ have order dividing $n$ (see Problem 14.53 of [The Kourovka Notebook, No. 19, 2019]). \\ The validity of the conjecture has been proved in [Arch. Math. (Basel) 75 (2000) 1-7] for $n=2$. Here we confirm the conjecture for $n=3$.

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