منابع مشابه
Solving equations in free nilpotent groups
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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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 ...
متن کاملNilpotent Groups
The articles [2], [3], [4], [6], [7], [5], [8], [9], [10], and [1] provide the notation and terminology for this paper. For simplicity, we use the following convention: x is a set, G is a group, A, B, H, H1, H2 are subgroups of G, a, b, c are elements of G, F is a finite sequence of elements of the carrier of G, and i, j are elements of N. One can prove the following propositions: (1) ab = a · ...
متن کاملComputing twisted conjugacy classes in free groups using nilpotent quotients
There currently exists no algebraic algorithm for computing twisted conjugacy classes in free groups. We propose a new technique for deciding twisted conjugacy relations using nilpotent quotients. Our technique is a generalization of the common abelianization method, but admits significantly greater rates of success. We present experimental results demonstrating the efficacy of the technique, a...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2010
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196710005819