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[Eric Murphy]

by S Sarkar 2004 Cited by 3 Abstract Let F2 be the free group generated by x and y. In this article, we prove that the commutator of xm and yn is a product of two squares if.. It is straightforward to write down the Schreier generators of a subgroups of finite index of a group given by a finite presentation. When the group is free, th.. by N GUPTA Cited by 3 For fixed m, n 2, we examine the structure of the nth lower central subgroup n(F) of the free group F of rank m with respect to a certain finite chain F = F(0).... by S Bachmuth 1965 Cited by 200 commutator subgroup. Then > = FF" will denote the free metabelian group of rank n. In this paper we will be considering those automorphisms of. by AM Gaglione 1975 Cited by 19 Every Fm is a free Abelian group of finite rank, Q(n). It has as a basis the images of the basic commutators of dimension n [4, 5, 181 under the homomorphism.. by A Putman 2021 Cited by 1 A beautifully simple free generating set for the commutator subgroup of a free group was constructed by Tomaszewski. We give a new geometric... 9ef30a34bc
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by TC Hurley 1990 Cited by 1 A FREE PRODUCT. T. C. HURLEY AND M. A. WARD. 1. Introduction. Let F = X* Y be the free product of a non-trivial group Y and a free group X. The groups [Y.... Abstract We show here that the commutator subgroup of a free group of finite rank poses a basis of Bachmuth's type.. by M Alizadeh Sanati In 1966, Stroud [2] proved that the commutator length of a free nilpotent group of rank is at most . After about twenty years, analogous result was obtained for free.... by EC Turner 1996 Cited by 110 that if an endomorphism of the free group of rank 2 fixes the commutator of a pair of generators, then it is an automorphism. This was improved by Zieschang.... by R Baer 1944 Cited by 53 powers of elements in G, or the commutator subgroup (G, G) of G which is ... Since G(0) is a finite group, there exists a free group G(l) on a finite number of ... Interesting relations between upper and lower central series f a finite -group have.... It is possible. Explanation: The classic example is the commutator subgroup of the free group on two generators. Let: G=. If g,hG then.... by VG Bardakov 2000 Cited by 10 We study commutator length in free groups. (By a commutator lengthcl(g) of an element g in a derived subgroup G of a group G we mean the least natur.. by M Auslander 1955 Cited by 81 Let [R, R] be the commutator subgroup of R, and let Fo = F/[R, R] and Ro RB/[R, B]. Then RB is a free abelian group of rank at least two. Moreover, the inner.
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