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Siberian Mathematical Journal, 2023
In this paper, a Frobenius group \(G\) is a semidirect product \(G=FH\) such that \(H \cap H^{g}=\{1\}\) for every \(g \in G \setminus H\) and \(F \setminus \{1\}=G \setminus \bigcup_{g \in G} H^{g}\). The normal subgroup \(F\) is the (Frobenius) kernel of \(G\) and \(H\) is the (Frobenius) complement of \(G\).
D. V. Lytkina, V. D. Mazurov
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In this paper, a Frobenius group \(G\) is a semidirect product \(G=FH\) such that \(H \cap H^{g}=\{1\}\) for every \(g \in G \setminus H\) and \(F \setminus \{1\}=G \setminus \bigcup_{g \in G} H^{g}\). The normal subgroup \(F\) is the (Frobenius) kernel of \(G\) and \(H\) is the (Frobenius) complement of \(G\).
D. V. Lytkina, V. D. Mazurov
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Mathematics of the USSR-Izvestiya, 1968
In this paper we construct an example of an infinite periodic group with a finite number of generators, in which the orders of all the elements are bounded by a specified number. This is a solution of the well-known Burnside problem.
P S Novikov, S I Adjan
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In this paper we construct an example of an infinite periodic group with a finite number of generators, in which the orders of all the elements are bounded by a specified number. This is a solution of the well-known Burnside problem.
P S Novikov, S I Adjan
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Infinite Groups of Finite Period
Algebra and Logic, 2015A first, important, result of this paper is that there exist periodic groups containing elements of even order and only trivial normal \(2\)-subgroups, in which every pair of involutions generates a \(2\)-group. This proves that, in general, the Baer-Suzuki theorem cannot be extended to periodic groups and gives a negative answer to Question 11.11a in ...
Mazurov, V. D. +2 more
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Minimally Almost Periodic Groups
The Annals of Mathematics, 1940Given 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, 2014Let \(G\) 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. +3 more
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