Effective results on the Waring problem for finite simple groups
نویسندگان
چکیده
منابع مشابه
A Refined Waring Problem for Finite Simple Groups
Let w1 and w2 be nontrivial words in free groups Fn1 and Fn2 , respectively. We prove that, for all sufficiently large finite nonabelian simple groups G, there exist subsets C1 ⊆ w1(G) and C2 ⊆ w2(G) such that |Ci | = O(|G|1/2 log |G|) and C1C2 = G. In particular, ifw is any nontrivial word and G is a sufficiently large finite nonabelian simple group, then w(G) contains a thin base of order 2. ...
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The classical Waring problem deals with expressing every natural number as a sum of g(k) k powers. Similar problems were recently studied in group theory, where we aim to present group elements as short products of values of a given word w 6= 1. In this paper we study this problem for Lie groups and Chevalley groups over infinite fields. We show that for a fixed word w 6= 1 and for a classical ...
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15 صفحه اولSome numerical results on two classes of finite groups
In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2015
ISSN: 1080-6377
DOI: 10.1353/ajm.2015.0035