| Autor: |
Malekan, Meisam Soleimani, Abdollahi, Alireza, Ebrahimi, Mahdi |
| Rok vydání: |
2020 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 study the conjecture for compact groups $G$ which are not necessarily profinite and $n=3$; we show that in the latter case the group $G$ contains an open normal $2$-Engel subgroup. |
| Databáze: |
arXiv |
| Externí odkaz: |
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