Results 261 to 270 of about 6,050,140 (310)
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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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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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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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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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Imbedding of periodic groups in simple periodic groups
Ukrainian Mathematical Journal, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON PERIODIC PRODUCTS OF GROUPS
International Journal of Algebra and Computation, 1995Adian introduced periodic n-products of groups which are given by imposing of defining relations of the form An=1 on the free product [Formula: see text] of groups Gα, α∈I, without involutions. The defining relations An=1 are constructed by a complicated induction which is quite similar to the inductive construction of free Burnside groups due to ...
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On the Product of Subsets in Periodic Groups
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2022Let \(S\) be a finite subset of a group \(G\). Denote the set of all-possible products of the form \(a_1\cdot a_t\), where \(a_i\in S\) by \(S^{t}\). \textit{M.-C. Chang} [J. Inst. Math. Jussieu 7, No. 1, 1--25 (2008; Zbl 1167.20328)] proved that for any finite subset of the free group not belonging to any cyclic subgroup, there exist constants \(c ...
Atabekyan, V. S., Mikaelyan, V. G.
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Nonunitarizable periodic groups
Mathematical Notes, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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PERIODIC FACTOR GROUPS OF HYPERBOLIC GROUPS
Mathematics of the USSR-Sbornik, 1992Summary: 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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