Group rings with solvable $n$-Engel unit groups

Group Rings with Solvable «-engel Unit Groups'

Let KG be the group ring of a group G over a field of characteristic p > 0, p ^ 2, 3. Suppose G contains no element of order p (if p > 0). Group algebras KG with unit group U(KG) solvable and n-Engel are characterized. Let ATG be the group ring of a group G over a field K of characteristic p > 0 and let U(KG) denote its group of units. Several authors including Bateman [1], Bateman and Coleman ...

Robert Fitzgerald Morse: Solvable Engel Groups 1 Solvable Engel Groups with Nilpotent Normal Closures

In this paper we investigate certain solvable (n+1)-Engel groups and bounded left Engel groups. We show that these (n + 1)-Engel groups can be characterized as those groups in which the normal closure of each element in the group is nilpotent of class at most n. Similarly, the bounded left Engel groups investigated can be characterized as those groups in which the normal closure of each element...

Group 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...

Engel-like Identities Characterizing Finite Solvable Groups

Engel-like Identities Characterising Finite Solvable Groups