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On locally primitive Cayley graphs of finite simple groups

Journal of Combinatorial Theory - Series A, 2011
In this paper we investigate locally primitive Cayley graphs of finite nonabelian simple groups. First, we prove that, for any valency d for which the Weiss conjecture holds (for example, d⩽20 or d is a prime number by Conder, Li and Praeger (2000) [1]),
Xingui Fang, Ma, Xuesong, Fang, Xingui, Xuesong Ma, Jie Wang, Wang, Jie   +5 more
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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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On local categories of finite groups

Mathematische Zeitschrift, 2011
Let \(\mathcal P\) be a partially ordered set and let \(G\) be a group. Then \(\mathcal P\) is a \(G\)-poset if there is a group homomorphism \(G\to\Aut(\mathcal P)\) giving an action of \(G\) on \(\mathcal P\). The transporter category \(G\propto\mathcal P\) has the same objects as \(\mathcal P\) and morphisms from \(x\) to \(y\) are couples \((g,gx ...
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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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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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On a class of locally finite T-groups

Forum Mathematicum, 2007
The authors are concerned with the class of radical locally finite groups satisfying min-\(p\) for all primes \(p\) and denoted by \(c\overline{\mathcal L}\). The Wielandt subgroup, \(\omega(G)\), of a group \(G\), is the intersection of all normalizers of subnormal subgroups of \(G\) and a group \(G\) is called a \(T\)-group precisely when normality ...
Ballester-Bolinches, Adolfo, Heineken, Hermann, Pedraza, Tatiana   +2 more
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The Behaviour of Homology in the Localization of Finite Groups

Canadian Mathematical Bulletin, 1991
AbstractWe show that, for a finite group G and a prime p, the following facts are equivalent: (i) the p-localization homomorphism l: G —> Gp induces p-localization on integral homology; (ii) the higher homotopy groups of the Bousfield-Kan Zp-completion of a K(G, 1) vanish; (iii) the group G is p-nilpotent.
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Sylow Subgroups of Locally Finite Groups

Proceedings of the London Mathematical Society, 1971
The theorems of Sylow are among the most basic in the theory of finite groups, and Hall’s theorems on the existence and conjugacy of Hall π-subgroups occupy a similarly central position in the theory of finite soluble groups. It is therefore natural to ask for what kinds of infinite groups results like them are true, and to what extent other parts of ...
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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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ZF and Locally Finite Groups

Mathematical Logic Quarterly, 1981
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