منابع مشابه
on the right n-engel group elements
in this paper we study right $n$-engel group elements. by modifying a group constructed by newman and nickel, we construct, for each integer $ngeq 5$, a 2-generator group $g =langle a, brangle$ with the property that $b$ is a right $n$-engel element but where $[b^k,_n a]$ is of infinite order when $knotin {0, 1}$.
متن کاملon the probability of being a 2-engel group
let $g$ be a finite group and $d_2(g)$ denotes the probability that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $g$. we will obtain lower and upper bounds for $d_2(g)$ in the case where the sets $e_g(x)={yin g:[y,x,x]=1}$ are subgroups of $g$ for all $xin g$. also the given examples illustrate that all the bounds are sharp.
متن کاملon the probability of being a $2$-engel group
let $g$ be a finite group and $d_2(g)$ denotes the probability that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $g$. we will obtain lower and upper bounds for $d_2(g)$ in the case where the sets $e_g(x)={yin g:[y,x,x]=1}$ are subgroups of $g$ for all $xin g$. also the given examples illustrate that all the bounds are sharp.
متن کاملGroup rings satisfying generalized Engel conditions
Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1) y]=[[x ,_( n) y] , y]. In this paper we show that necessary and sufficient conditions for RG to satisfies [x^m(x,y) ,_( n(x,y)) y]=0 is: 1) if r is a power of a prime p, then G is a locally nilpotent group an...
متن کاملEngel Graph Associated with a Group
Let G be a non-Engel group and let L(G) be the set of all left Engel elements of G. Associate with G a graph EG as follows: Take G\L(G) as vertices of EG and join two distinct vertices x and y whenever [x,k y] 6= 1 and [y,k x] 6= 1 for all positive integers k. We call EG, the Engel graph of G. In this paper we study the graph theoretical properties of EG.
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1959
ISSN: 0019-2082
DOI: 10.1215/ijm/1255455117