Corpus ID: 229679855

Profinite groups with many elements of bounded order

@inproceedings{Abdollahi2020ProfiniteGW,
  title={Profinite groups with many elements of bounded order},
  author={A. Abdollahi and Meisam Soleimani Malekan},
  year={2020}
}
Lévai and Pyber proposed the following as a conjecture: Let G be a profinite group such that the set of solutions of the equation xn = 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. 

References

SHOWING 1-7 OF 7 REFERENCES
Compact groups with many elements of bounded order
Abstract Lévai and Pyber proposed the following as a conjecture: Let G be a profinite group such that the set of solutions of the equation xn=1{x^{n}=1} has positive Haar measure. Then G has an openExpand
Profinite groups with many commuting pairs or involutions
Abstract. We prove that if the set of commuting pairs of a profinite group G has positive Haar measure then G is abelian by finite. Using this we show that the set I of involutions has positiveExpand
Groups in which a large number of operators may correspond to their inverses
An abelian group may be defined by the property that, in an automorphism of the group, more than three fourths its operators may be placed in a one to one correspondence with their inverses.t It mayExpand
Largeur et nilpotence
The notion of a large set in an arbitrary group is introduced in analogy to the generic sets in an algebraic or stable group. The question is studied which properties “satisfied largely” by a groupExpand
Finiteness conditions and generalized soluble groups
1. Fundamental Concepts in the Theory of Infinite Groups.- 2. Soluble and Nilpotent Groups.- 3. Maximal and Minimal Conditions.- 4. Finiteness Conditions on Conjugates and Commutators.- 5. FinitenessExpand
Largeness and equational probability in groups
We define k-genericity and k-largeness for a subset of a group, and determine the value of k for which a k-large subset of G^n is already the whole of G^n , for various equationally defined subsets.Expand
Unsolved problems in group theory. The Kourovka notebook. No. 18
This is a collection of open problems in Group Theory proposed by more than 300 mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1965, now also inExpand