منابع مشابه
Powers in finite groups
If G is a finitely generated profinite group then the verbal subgroup Gq is open. In a d-generator finite group every product of qth powers is a product of f(d, q) qth powers. 20E20, 20F20.
متن کاملStrongly Bounded Groups and Infinite Powers of Finite Groups
We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by Bergman. Our main result is that G is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that ω1-existentia...
متن کاملPowers in finite fields
There are lots of results on the “random-like” behaviour of square elements in finite fields. For example, they can be used in combinatorial constructions and algorithms, as their properties somehow “imitate” a random distribution. In this paper we investigate the more general question concerning the behaviour of d-th powers in finite fields (where d is a fixed value). Surprisingly, they are di...
متن کاملPowers in Finitely Generated Groups
In this paper we study the set Γn of nth-powers in certain finitely generated groups Γ. We show that, if Γ is soluble or linear, and Γn contains a finite index subgroup, then Γ is nilpotent-by-finite. We also show that, if Γ is linear and Γn has finite index (i.e. Γ may be covered by finitely many translations of Γn), then Γ is soluble-by-finite. The proof applies invariant measures on amenable...
متن کاملPairwise non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups
Let $G$ be a finite group. A subset $X$ of $G$ is a set of pairwise non-commuting elements if any two distinct elements of $X$ do not commute. In this paper we determine the maximum size of these subsets in any finite non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2011
ISSN: 1661-7207
DOI: 10.4171/ggd/136