Solvable Groups

Author(s):  
Tullio Ceccherini-Silberstein ◽  
Michele D’Adderio
Keyword(s):  
Author(s):  
Olaf Manz ◽  
Thomas R. Wolf
Keyword(s):  

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiakuan Lu ◽  
Kaisun Wu ◽  
Wei Meng

AbstractLet 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1_{H})^{G} for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.


1984 ◽  
Vol 87 (1) ◽  
pp. 222-246 ◽  
Author(s):  
David Gluck ◽  
Thomas R Wolf

1969 ◽  
Vol 5 (3) ◽  
pp. 233-237
Author(s):  
B. A. Kramarev
Keyword(s):  

1971 ◽  
Vol 23 (1) ◽  
pp. 12-21
Author(s):  
J. Malzan

If ρ(G) is a finite, real, orthogonal group of matrices acting on the real vector space V, then there is defined [5], by the action of ρ(G), a convex subset of the unit sphere in V called a fundamental region. When the unit sphere is covered by the images under ρ(G) of a fundamental region, we obtain a semi-regular figure.The group-theoretical problem in this kind of geometry is to find when the fundamental region is unique. In this paper we examine the subgroups, ρ(H), of ρ(G) with a view of finding what subspace, W of V consists of vectors held fixed by all the matrices of ρ(H). Any such subspace lies between two copies of a fundamental region and so contributes to a boundary of both. If enough of these boundaries might be found, the fundamental region would be completely described.


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