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L. Babai, V. Sós (1985)
Sidon Sets in Groups and Induced Subgraphs of Cayley GraphsEur. J. Comb., 6
B. Neumann (1954)
Groups Covered By Permutable SubsetsJournal of The London Mathematical Society-second Series
B. Neumann, Jennifer Wallis (1976)
A problem of Paul Erdös on groupsJournal of the Australian Mathematical Society, 21
(1954)
NEUMANN, 'Groups covered by permutable subsets
ON DEFICIENT SQUARES GROUPS AND FULLY- INDEPENDENT SUBSETS MARCEL HERZOG AND CARLO M. SCOPPOLA 1. Introduction In 1976, B. H. Neumann [4] characterized the central-by-finite groups by the following property: the group G is central-by-finite if and only if it does not contain an infinite independent subset, where a subset U of G is called independent if uv = vu for u,veUimplies u = v. More recently, P. Longobardi, M. Maj and the first author [2] considered a more general class of groups, the deficient squares groups. A group is said to satisfy the deficient squares property if there exists an integer m such that 2 2 \M*\ < |A/j for all subsets M of G of size m, where M = {mn \m,ne M). They showed that a group G satisfies the deficient squares property if and only if one of the following holds: G is central-by-finite, |{g |ge(j}| is finite, or G is nearly dihedral, where by nearly dihedral we mean a group G with an abelian normal subgroup H of finite index, on which each element of G acts by conjugation either as the identity automorphism or as the inverting automorphism. The aim of this paper
Bulletin of the London Mathematical Society – Wiley
Published: Jan 1, 1995
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