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On Groups with Extreme Centralizers and Normalizers [PDF]
Advances in Group Theory and Applications, 2016 An FCI-group is a group in which every non-normal cyclic subgroup has finite index in its centralizer and an FNI-group is one in which every non-normal subgroup has finite index in its normalizer.
Derek J.S. Robinson
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Finite and Locally Finite Groups [PDF]
, 1995 Preface. Introduction. Simple locally finite groups B. Hartley. Algebraic groups G.M. Seitz. Subgroups of simple algebraic groups and related finite and locally finite groups of Lie type M.W. Liebeck. Finite simple groups and permutation groups J. Saxl. Finitary linear groups: a survey R.E. Phillips.
Hartley, B. +3 more
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Journal of Algebra, 1984 This paper is a contribution to the study of locally finite groups satisfying Min-2, the minimal condition on 2-subgroups. Such a group G is called 2-fine, if the Sylow 2-subgroups of \(G/0_{2'2}(G)\) are finite. Conditions for a locally finite group with Min-2 to be 2-fine are important because they often enable problems about such groups to be ...
Stingl, Volker, Turau, Volker
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Chevalleyp–local finite groups [PDF]
Algebraic & Geometric Topology, 2007 This paper is an impressive contribution to the theory of \(p\)-local finite groups with a number of very interesting results, including the following two theorems: Theorem A: Let \(p\) be an odd prime. If \(X\) is a \(1\)-connected \(p\)-compact group, \(q\) a prime power prime to \(p\), and \(\tau\) an automorphism of \(X\) of finite order prime to \(
Møller, Jesper Michael, Broto, Carles
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Locally finite groups of finite centralizer dimension [PDF]
Journal of Group Theory, 2019 Abstract We describe the structure of locally finite groups of finite centralizer dimension.
Borovik, Alexandre, Karhumäki, Ulla
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Extensions of $p$-local finite groups [PDF]
Transactions of the American Mathematical Society, 2007 A p-local finite group consists of a finite p-group S, together with a pair of categories which encode ``conjugacy'' relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying ...
Broto, Carles +4 more
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Nilpotent $p$-local finite groups
, 2011 In this paper we prove characterizations of $p$-nilpotency for fusion systems and $p$-local finite groups that are inspired by results in the literature for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
Cantarero, J., Scherer, J., Viruel, A.
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Complete Universal Locally Finite Groups [PDF]
Transactions of the American Mathematical Society, 1978 This paper will partly strengthen a recent application of model theory to the construction of sets of pairwise nonembeddable universal locally finite groups [8]. Our result is Theorem. There is a set U \mathcal {U} of 2 ℵ 1
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Sylowizers in Locally Finite Groups [PDF]
Proceedings of the American Mathematical Society, 1974 A result of W. Gaschütz for finite soluble groups is extended to two classes of locally finite, locally soluble groups.
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ON LOCAL FINITENESS OF PERIODIC RESIDUALLY FINITE GROUPS [PDF]
Proceedings of the Edinburgh Mathematical Society, 2002 AbstractLet $G$ be a periodic residually finite group containing a nilpotent subgroup $A$ such that $C_G(A)$ is finite. We show that if $\langle A,A^g\rangle$ is finite for any $g\in G$, then $G$ is locally finite.AMS 2000 Mathematics subject classification: Primary ...
Kuzucuoğlu, Mahmut, Shumyatsky, Pavel
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