منابع مشابه
On palindromic width of certain extensions and quotients of free nilpotent groups
In [3] the authors provided a bound for the palindromic width of free abelianby-nilpotent group ANn of rank n and free nilpotent group Nn,r of rank n and step r. In the present paper we study palindromic widths of groups ÃNn and Ñn,r . We denote by G̃n = Gn/〈〈x21, . . . , x 2 n 〉〉 the quotient of group Gn = 〈x1, . . . , xn〉, which is free in some variety by the normal subgroup generated by x 1 ,...
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We examine the palindromic automorphism group ΠA(Fn) of a free group Fn, a group first defined by Collins in [5] which is related to hyperelliptic involutions of mapping class groups, congruence subgroups of SLn(Z), and symmetric automorphism groups of free groups. Cohomological properties of the group are explored by looking at a contractible space on which ΠA(Fn) acts properly with finite quo...
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Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...
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In this paper we show that any system of equations over a free nilpotent group of class c is either unitary or nullary. In fact, such a system either has a most general solution (akin to the most general solution of a system of linear diophantine equations), or every solution has a proper generalization. In principle we provide an algorithm for determining whether or not a most general solution...
متن کاملCommutators and Squares in Free Nilpotent Groups
In a free group no nontrivial commutator is a square. And in the free group F2 = F (x1, x2) freely generated by x1, x2 the commutator [x1, x2], is never the product of two squares in F2, although it is always the product of three squares. Let F2,3 = 〈x1, x2〉 be a free nilpotent group of rank 2 and class 3 freely generated by x1, x2. We prove that in F2,3 = 〈x1, x2〉, it is possible to write cert...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.12.002