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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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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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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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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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Mathematics of the USSR-Izvestiya, 1983
An algorithm for recognizing the solvability of arbitrary equations in a free group is constructed. Bibliography: 11 titles.
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An algorithm for recognizing the solvability of arbitrary equations in a free group is constructed. Bibliography: 11 titles.
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PSEUDOCHARACTERS ON FREE GROUPS
Russian Academy of Sciences. Izvestiya Mathematics, 1995Let \(G\) be a group. A real function \(\varphi\) from \(G\) is called a pseudocharacter if there exists an \(\varepsilon > 0\) such that \(|\varphi (xy) - \varphi (x) - \varphi (y)|< \varepsilon\) for any \(x, y \in G\) and \(n \varphi (x) = \varphi (x^n)\) for any \(x \in G\) and any integer \(n\).
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Free Subgroups of Free Topological Groups
1974It is well known that every subgroup of a free group is a free group. However, it is not true in general that a subgroup of a free topological group is a free topological group.
David C. Hunt, Sidney A. Morris
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Carrier-free nanomedicines for cancer treatment
Progress in Materials Science, 2022Li-Han Liu, Xian-Zheng Zhang
exaly