Results 301 to 310 of about 21,501,912 (352)
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Primitivity in Free Groups and Free Metabelian Groups
Canadian Journal of Mathematics, 1992AbstractLet Mn, c denote the free n-generator metabelian nilpotent group of class c. For m ≤ n – 2, every primitive system of m elements of Mn, c can be lifted to a primitive system of m elements of the absolutely free group Fn of rank n. The restriction on m cannot be improved.
Gupta, C. K. +2 more
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International Journal of Algebra and Computation, 2004
This paper deals with the study of the free noncommutative group in the multiplicative group of the skewfield of the real Hamilton quaternions. The main results proved in this paper allows us to obtain the following interesting corollary: let G be a subgroup of rational quaternions. Then G is either solvable or contains the free noncommutative group.
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This paper deals with the study of the free noncommutative group in the multiplicative group of the skewfield of the real Hamilton quaternions. The main results proved in this paper allows us to obtain the following interesting corollary: let G be a subgroup of rational quaternions. Then G is either solvable or contains the free noncommutative group.
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Applied Categorical Structures, 2010
There is given a condition for the existence of free internal groups which generalizes and unifies known results.
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There is given a condition for the existence of free internal groups which generalizes and unifies known results.
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Context-Free Groups and Bass–Serre Theory
, 2013The word problem of a finitely generated group is the set of words over the generators that are equal to the identity in the group. The word problem is therefore a formal language.
V. Diekert, A. Weiss
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Canadian Mathematical Bulletin, 1981
We study the representations of an element of a free group as a commutator. For a given element g of a free group F, we are interested in the set of all pairs (x, y) of elements of F such that(1)where [x, y] = xyx-1 y-1. If g = 1, the problem is trivial. We assume henceforth that g ≠ 1.
Lyndon, R. C., Wicks, M. J.
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We study the representations of an element of a free group as a commutator. For a given element g of a free group F, we are interested in the set of all pairs (x, y) of elements of F such that(1)where [x, y] = xyx-1 y-1. If g = 1, the problem is trivial. We assume henceforth that g ≠ 1.
Lyndon, R. C., Wicks, M. J.
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Free Groups and Free Products of Groups
1991In the preceding chapters we have introduced the fundamental group of a space and actually determined its structure in some of the simplest cases. In more complicated cases we need a larger vocabulary and a greater knowledge of group theory to describe its structure and actually to make use of its properties.
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The Mathematical Intelligencer, 1992
By taking appropriate concrete functions on the complex or real numbers, in this nicely written survey the author shows that free groups and free products of groups occur naturally and explicitly. We just mention two of the results surveyed: \textit{S. A. Adeleke, A. M. W. Glass} and \textit{L. Morley} [J. Lond. Math. Soc., II. Ser. 43, No. 2, 255-268 (
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By taking appropriate concrete functions on the complex or real numbers, in this nicely written survey the author shows that free groups and free products of groups occur naturally and explicitly. We just mention two of the results surveyed: \textit{S. A. Adeleke, A. M. W. Glass} and \textit{L. Morley} [J. Lond. Math. Soc., II. Ser. 43, No. 2, 255-268 (
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