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such that, for fixed positive integers r and s, xr commutes with (xs)y for all x,y∈G. Various general bounds are proved for the structure of groups in the corresponding variety, defined by the law [Xr,(Xs)Y]=1. ...
AbstractShumyatsky and the second author proved that if G is a finitely generated residually finite p- group satisfying a law , then, for almost all primes p, the fact that a normal and commutator ...
such that, for fixed positive integers r and s, xr commutes with (xs)y for all x,y∈G. Various general bounds are proved for the structure of groups in the corresponding variety, defined by the law [Xr,(Xs)Y]=1. A group ...
commutative objects, which are precisely the preordered groups whose group law is commutative . The second one is the category of abelian objects, that turns out to be the category of monomorphisms ...
associative system. We shallassume that the additive group is commutative . If both semigroups of a semiring are commutative , we say that the semiring is commutative . Definition 1. A halfring H is a semiring ...
The work is inspired by a question of R. Burns: What do the Engel laws and positive laws have in common that forces finitely generated, locally graded groups satisfying them to be nilpotent-by-finite ...
B.H. Neumann recently proved some implications for semigroup laws in groups . This may help in the solution of a problem posed by G.M. Bergman in 1981. BULL. AUSTRAL. MATH. SOC. 20E10, 20M07 VOL. 65 ...
to that in the class of virtually pro-$p$ groups . This is used to show that if $q,n$ are positive integers and $w$ is a multilinear commutator word, then the words $w^q$ and $[w^q,_{n} y]$ are concise in residually ...
Homeira Pajoohesh Abstract. In this article, we give a positive answer to the open problem of whether L ∩A = E holds for every n. n n 1. Introduction A lattice ordered group (- group ) is a group ...
{\infty}$, and the expectation functional used on the group algebra of $S_{\infty}$ depends in a natural way on a parameter $d$, which is a positive integer. We identify precisely the limit distribution ...
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