منابع مشابه
Twisted Group Rings of Metacyclic Groups
Given a finite metacyclic group G, a central extension F having the projective lifting property over all fields is constructed. This extension and its group rings are used to investigate the faithful irreducible projective representations of G and the fields over which they can be realized. A full description of the finite metacyclic groups having central simple twisted group rings over fields ...
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Suppose that a finite group G admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup CG(H) of the complement is nilpotent of class c. It is proved that G has a nilpotent characteristic subgroup of index bounded in terms of c, |CG(F )|, and |F | whose nilpotency class is bounded in terms of c and |H| only. This gener...
متن کاملThe Dade group of a metacyclic p-group
The Dade group D(P ) of a finite p-group P , formed by equivalence classes of endopermutation modules, is a finitely generated abelian group. Its torsion-free rank equals the number of conjugacy classes of non-cyclic subgroups of P and it is conjectured that every nontrivial element of its torsion subgroup D(P ) has order 2, (or also 4, in case p = 2). The group D(P ) is closely related to the ...
متن کاملAutomorphisms of Metacyclic p-Groups With Cyclic Maximal Subgroups
This paper deals with the determination of the automorphism group of the metacyclic p-groups, P (p,m), given by the presentation P (p,m) = 〈x, y|xpm = 1, y = 1, yxy−1 = xp+1〉 (1) where p is an odd prime number and m > 1. We will show that Aut(P ) has a unique Sylow p-subgroup, Sp, and that in fact
متن کاملHilbert Functions of Finite Group Orbits: Abelian and Metacyclic Groups
This thesis is concerned with Hilbert functions of ideals of finite group orbits, focusing in particular on abelian and metacyclic groups. Conjecture 16 in Section 4 characterizes the Hilbert functions that arise from two-dimensional representations of certain abelian groups, and a proof of the necessity of its conditions is provided. In Section 6, Proposition 18 gives a bound for the Hilbert f...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1976
ISSN: 0386-2194
DOI: 10.3792/pja/1195518295