Positive laws on word values in residually-p groups
نویسندگان
چکیده
منابع مشابه
Some Residually Finite Groups Satisfying Laws
We give an example of a residually-p finitely generated group, that satisfies a non-trivial group law, but is not virtually solvable. Denote by Fn the free group on n generators. Recall that, given a group word m(x1, . . . , xn) ∈ Fn, a group G satisfies the law m = 1 if for every u1, . . . , un ∈ G, m(u1, . . . , un) = 1. Given a set S of group laws, the n-generator free group in the variety g...
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Let w = w(x1, ..., xd) denote a group word in d variables, that is, an element of the free group of rank d. For a finite group G we may define a word map that sends a d-tuple, (g1, ..., gd) of elements of G, to its w-value, w(g1, ..., gd), by substituting variables and evaluating the word in G by performing all relevant group operations. In this thesis we study a number of problems to do with t...
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We give negative answers to three questions concerning positive laws and ApA varieties. Let A denote the variety of all abelian groups and Ap — the variety of all abelian groups of exponent p. By F we denote a free group and by V — a verbal subgroup in F . We write G ⊇ F to say that G contains a free nonabelian subsemigroup. A variety generated by G is denoted by var(G). A law u(x1, ..., xn) = ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2015
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.12.005