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On permutation groups of finite type
No full textAbstractA permutation group G is said to be a group of finite type { k }, k a positive integer, if each non-identity element of G has exactly k fixed points. We show that a group G can be faithfully represented as an irredundant permutation group of finite type if and only if G has a non-trivial normal partition such that each component has finite bounded index in its normalizer. An asymptotic structure theorem for locally (soluble-by-finite) groups of finite type is proved. Finite sharp irredundant permutation groups of finite type, notp -groups, are determined
Non-abelian sharp permutation -groups
No full textAbstractA permutation group G of finite degree n is a sharp irredundant group of type {k}, k a positive integer, if each non-identity element of G fixes exactly k points, |G|=n−k and G has no global fixed point and no regular orbit. In this note we give a method to construct all faithful representations of finite abelian groups as sharp irredundant permutation groups of type {k} for some positive integer k
On minimal degrees of permutation representations of abelian quotients of finite groups
Get PDFAbstractFor a finite group G, we denote by μ(G) the minimum degree of a faithful permutation representation of G. We prove that if G is a finite p-group with an abelian maximal subgroup, then μ(G/G′)≤μ(G).</jats:p
A charaterization of : addendum
No full textWe give a characterisation of the sporadic simple group of Harada-Norton as group of local characteristic and local characteristic , with a prime greater than
A characterization of HN
No full textIn a typical finite simple group of Lie type the defining characteristic is easily recognisable from the subgroup structure, since the maximal -local subgroups look completely different from the maximal -local subgroups, where is any prime other than . There are various ways of abstracting these properties of the -local subgroups, which play an important role in both the description and the classification of the finite simple groups. Such abstract definitions of `characteristic' usually assign the alternating groups no characteristic at all, whereas some of the sporadic simple groups have two or more characteristics.\par The Harada-Norton group seems in this way to have characteristics , , and . The main theorem of the paper under review is that is characterised by certain conditions on the -local and -local subgroups (the -local subgroups are not mentioned), which roughly say that the group is of bicharacteristic .
[Robert Wilson (London)
Permutation modules for the symmetric group
Full text linkIn this paper we present a general method for computing the irreducible components of the permutation modules of the symmetric groups over a field of characteristic 0. We apply this machinery to determine the decomposition into irreducible submodules of the -permutation module on the right cosets of the normaliser in of the subgroup generated by a permutation of type
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