On the reconstruction index of permutation groups: semiregular groups
نویسندگان
چکیده
منابع مشابه
Transitive Permutation Groups without Semiregular Subgroups
A transitive finite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main results are recursive constructions of elusive permutation groups, using various product operations and affine group constructions. A brief historical introduction and a survey of known elusive groups a...
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A nonidentity element of a permutation group is said to be semiregular if all of its orbits have the same length. The work in this paper is linked to [6] where the problem of existence of semiregular automorphisms in vertex-transitive digraphs was posed. It was observed there that every vertex-transitive digraph of order pk or mp, where p is a prime, k 1 and m p are positive integers, has a sem...
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About 60 years ago H. Zassenhaus 17] classiied nite near-elds. In doing so he also gave a full description of those nite groups which have a representation D (over C) such that D(g) has no eigenvalue 1 for any nontrivial element g 2 G. In our terminology such a group is called semiregular. One of the results in 17] characterizes SL 2 (5) as the only perfect semiregular group. Clearly, if the un...
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By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
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We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.
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ژورنال
عنوان ژورنال: Aequationes Mathematicae
سال: 2002
ISSN: 0001-9054
DOI: 10.1007/pl00012404