Results 221 to 230 of about 19,909 (248)

INVOLUTIONS IN LOCALLY FINITE GROUPS

Journal of the London Mathematical Society, 2004
Summary: The paper deals with locally finite groups \(G\) having an involution \(\varphi\) such that \(C_G(\varphi)\) is of finite rank. The following theorem gives a very detailed description of such groups. Let \(G\) be a locally finite group having an involution \(\varphi\) such that \(C_G(\varphi)\) is of finite rank.
Kuzucuoğlu, Mahmut, Shumyatsky, Pavel
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σ-Subnormality in locally finite groups

Journal of Algebra, 2023
Let \(\sigma=\{\sigma_{j} \mid j \in J\}\) be a partition of the set of prime numbers. A subgroup \(X\) of a finite group \(G\) is \(\sigma\)-subnormal if there exists a chain of subgroups \(X=X_{0} \leq X_{1} \leq \dots \leq X_{n}=G\) such that, for each \(1 \leq i \leq n\), \(X_{i-1} \trianglelefteq X_{i}\) or \(X_{i}/(X_{i-1})_{X_{i}}\) is a ...
Ferrara M., Trombetti M.
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Locally Finite Barely Transitive Groups

Algebra and Logic, 2003
Infinite transitive permutation groups all proper subgroups of which have just finite orbits are treated. Under the extra condition of being locally finite, such groups are proved to be primary, and, moreover, soluble if the stabilizer of some point is soluble.
Belyaev, V. V., Kuzucuoglu, Mahmud
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On Infinite Locally Finite Groups

Canadian Mathematical Bulletin, 1994
AbstractIf G is a group such that every infinite subset of G contains a commuting pair of elements then G is centre-by-finite. This result is due to B. H. Neumann. From this it can be shown that if G is infinite and such that for every pair X, Y of infinite subsets of G there is some x in X and some y in Y that commute, then G is abelian. It is natural
Rhemtulla, Akbar, Smith, Howard
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Locally Finite Simple Groups

1974
The group G is locally finite if each of its finitely generated subgroups is finite. Until rather recently the area of locally finite groups entirely belonged to the wilderness of counter-examples; and there absurdly wild behaviour is possible, indeed. What little progress has been made in cultivating some fringes of this wilderness is essentially due ...
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Local Covering Subgroups in Finite Groups

Acta Mathematica Sinica, English Series, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Locally Finite Suzuki–Higman 2-Groups

Algebra and Logic, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Locally Finite-Indicable Groups

Communications in Algebra, 2007
A group is locally ℜ-indicable if every finitely generated subgroup has a nontrivial homomorphism onto a nontrivial ℜ-group. If ℜ is a quasi-variety, then the class L(ℜ) of locally ℜ-indicable groups coincides with the class N(ℜ) of groups which have normal systems with factors in ℜ.
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Local Finite Group Theory

1982
The word local is used in finite group-theory in relation to a fixed prime p; thus properties of p-subgroups or their normalisers, for example, are regarded as local. In the case of a soluble group, then, everything is local, but an insoluble group also has global aspects.
Bertram Huppert, Norman Blackburn
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Locally Finite Representations of Polycyclic-by-Finite Groups

Proceedings of the London Mathematical Society, 1982
From the introduction: ``Let \(G\) be a polycyclic-by-finite group, \(k\) a field, and \(V\) a right \(kG\)-module of finite \(k\)-dimension. This work was motivated by Musson's result [in I. M. Musson, Q. J. Math., Oxf. II. Ser. 31, 429--448 (1980; Zbl 0413.16012)], that if \(k\) has positive characteristic then the injective hull \(E(V)\) of \(V\) is
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