Results 271 to 280 of about 218,992 (317)

Minimally Almost Periodic Groups

The Annals of Mathematics, 1940
Given a group g it is of some interest to decide which elements of g can be “told apart” by almost periodic functions of g or, which is the same thing (cf. below) by finite dimensional bounded linear representations of g. That is: For two a, b ∈ g we define a ~ b by either of these two properties: (I) For every almost periodic function f(x) in g
von Neumann, J., Wigner, Eugene P.
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Periodic groups acting freely on abelian groups

Proceedings of the Steklov Institute of Mathematics, 2014
Let \(G\) be a periodic group and let \(\pi\) be a set of primes, then \(G\) is called a \(\pi\)-group if all prime divisors of the order of each element of \(G\) lie in \(\pi\). The subgroup generated by elements of prime order of \(G\) is denoted by \(\Omega(G)\).
Zhurtov, A. Kh., Lytkina, D. V., Mazurov, V. D., Sozutov, A. I.   +3 more
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Imbedding of periodic groups in simple periodic groups

Ukrainian Mathematical Journal, 1992
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Nonunitarizable periodic groups

Mathematical Notes, 2010
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PERIODIC FACTOR GROUPS OF HYPERBOLIC GROUPS

Mathematics of the USSR-Sbornik, 1992
Summary: It is proved that for any noncyclic hyperbolic torsion-free group \(G\) there exists an integer \(n(G)\) such that the factor group \(G/G^ n\) is infinite for any odd \(n \geq n(G)\). In addition, \(\bigcap^ \infty_{i = 1} G^ i = \{1\}\). (Here \(G^ i\) is the subgroup generated by the \(i\)th powers of all elements of the groups \(G\).).
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Imbedding of countable periodic groups into simple 2-generated periodic groups

Ukrainian Mathematical Journal, 1992
Summary: We prove a theorem on the isomorphic imbedding of an arbitrary countable periodic group \(H\) into a simple 2-generated periodic group \(G\). In addition, we show that for any integers \(k \geq 2\) and \(\ell \geq 3\) the group \(G\) contains a pair of generating elements whose orders are \(k\) and \(\ell\).
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Periodic groups acting freely on Abelian groups

Algebra and Logic, 2010
Let \(G\) be a group of automorphisms of a nontrivial group \(V\). The action of \(G\) on \(V\) is said to be `free' if \(v^g\neq v\) for every nontrivial \(g\in G\) and every nontrivial \(v\in V\). In this paper the author generalizes the following result by \textit{E. Jabara} and \textit{P. Mayr} [Forum Math. 21, No. 2, 217-220 (2009; Zbl 1177.20041)]
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A class of periodic groups

Algebra and Logic, 2005
A dihedral group is a group generated by two involutions. The authors call a group \(G\) saturated by dihedral groups, if every finite subgroup of \(G\) is contained in a dihedral subgroup of \(G\). First, the authors establish the structure of an arbitrary periodic group saturated by dihedral groups.
Shlepkin, A. K., Rubashkin, A. G.
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INVOLUTORY AUTOMORPHISMS OF PERIODIC GROUPS

International Journal of Algebra and Computation, 1996
Let \(G\) be a finite group of odd order, and let \(\varphi\) be an automorphism of order \(2\) of \(G\) such that the centralizer \(C_G(\varphi)\) is abelian. In this situation it has been proved by \textit{L. G. Kovács} and \textit{G. E. Wall} [Nagoya Math. J.
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Groups with periodic defining relations

Mathematical Notes, 2008
Let \(G\) be a group defined by finitely many relations of the form \(A_i^{n_i}=1\), where all the exponents \(n_i\) are divisible by an odd number \(n\geq 665\) and let \(G\) have no involutions. Then the author shows in this paper that the word and conjugacy problems are solvable for the above \(G\). In the proof, a way similar to that defined in the
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