scholarly journals p-Groups with an Abelian Maximal Subgroup and Cyclic Center

1976 ◽  
Vol 22 (2) ◽  
pp. 221-233 ◽  
Author(s):  
S. B. Conlon
Keyword(s):  
Maximal Subgroup ◽  
Automorphism Groups ◽  
Finite Subgroups

AbstractAll such nonabelian finite p-groups are classified. They coincide with the class of nonabelian finite p-subgroups of GL(p, F), where F is a field, not of characteristic p, which contains all p power roots of 1, or agian with the class of all nonabelian finite subgroups of Zp= wr Zp. Various automorphism groups associated to them and their representations are calculated. Two such subgroups of GL(p, F) are conjugate as subgroups of GL(p, F) iff they are isomorphic.

scholarly journals Dense locally finite subgroups of automorphism groups of ultraextensive spaces

2021 ◽  
Vol 391 ◽  
pp. 107966
Author(s):  
Mahmood Etedadialiabadi ◽  
Su Gao ◽  
François Le Maître ◽  
Julien Melleray
Keyword(s):  
Automorphism Groups ◽  
Locally Finite ◽  
Finite Subgroups

ON THE DIMENSION OF GROUPS THAT SATISFY CERTAIN CONDITIONS ON THEIR FINITE SUBGROUPS

2020 ◽  
pp. 1-6
Author(s):  
LUIS JORGE SÁNCHEZ SALDAÑA
Keyword(s):  
Maximal Subgroup ◽  
Modular Group ◽  
Cohomological Dimension ◽  
Finite Subgroup ◽  
Fuchsian Groups ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Finite Subgroups ◽  
One Relator Groups ◽  
Virtual Cohomological Dimension

Abstract We say a group G satisfies properties (M) and (NM) if every nontrivial finite subgroup of G is contained in a unique maximal finite subgroup, and every nontrivial finite maximal subgroup is self-normalizing. We prove that the Bredon cohomological dimension and the virtual cohomological dimension coincide for groups that admit a cocompact model for EG and satisfy properties (M) and (NM). Among the examples of groups satisfying these hypothesis are cocompact and arithmetic Fuchsian groups, one-relator groups, the Hilbert modular group, and 3-manifold groups.

Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

2020 ◽  
Vol 51 (4) ◽  
pp. 1919-1930
Author(s):  
Masoumeh Akbarizadeh ◽  
Mehdi Alaeiyan ◽  
Raffaele Scapellato
Keyword(s):  
Automorphism Groups

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

𝒫-characters and the structure of finite solvable groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiakuan Lu ◽  
Kaisun Wu ◽  
Wei Meng
Keyword(s):  
Finite Group ◽  
Maximal Subgroup ◽  
Solvable Group ◽  
Irreducible Character ◽  
Solvable Groups ◽  
Irreducible Constituent ◽  
A Finite Group

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.

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