Results 31 to 40 of about 1,123 (134)

On supersolvability of finite groups [PDF]

Glasgow Mathematical Journal, 2001
We prove a natural factorization of supersolvable groups and then we give another characterization of them in connection with the Fitting subgroup. Applying these theorems we describe the structure of some subclasses of supersolvable groups.
openaire   +2 more sources

Mutually Permutable Products of Finite Groups

International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011
Let G be a finite group and G1, G2 are two subgroups of G. We say that G1 and G2 are mutually permutable if G1 is permutable with every subgroup of G2 and G2 is permutable with every subgroup of G1. We prove that if G = G1G2 = G1G3 = G2G3 is the product of three supersolvable subgroups G1, G2, and G3, where Gi and Gj are mutually permutable for all i ...
Rola A. Hijazi, M. Asaad, G. Buskes, G. Mason, L. Vinet   +4 more
wiley   +1 more source

Antichain cutsets of strongly connected posets

, 2012
Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height.
A Aramova, A Björner, A Björner, A Björner, A Björner, A Björner, A Björner, A Hatcher, G Behrendt, I Rival, I Rival, J Ginsburg, M Bell, M Stern, P McNamara, RP Stanley, RP Stanley, RP Stanley, RP Stanley, Russ Woodroofe, Stephan Foldes   +20 more
core   +1 more source

Arrangements of ideal type

, 2017
In 2006 Sommers and Tymoczko defined so called arrangements of ideal type A_I stemming from ideals I in the set of positive roots of a reduced root system. They showed in a case by case argument that A_I is free if the root system is of classical type or
Roehrle, Gerhard
core   +1 more source

A note on p‐solvable and solvable finite groups

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 821-824, 1994., 1994
The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p‐solvable and solvable where p is the largest prime divisor of |G|. These are used further in identifying the largest normal p‐solvable and normal solvable subgroups, respectively, of G.
R. Khazal, N. P. Mukherjee
wiley   +1 more source

Maximal subgroups of finite groups

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 2, Page 311-314, 1990., 1989
In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting ...
S. Srinivasan
wiley   +1 more source

Evolving groups

, 2018
The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense.
Stanojkovski, Mima
core   +1 more source

A note on finite group structure influenced by second and third maximal subgroups

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 747-750, 1990., 1990
The structure of a finite group having specified number of second and third maximal subgroups has been investigated in the paper.
N. P. Mukherjee, R. Khazal
wiley   +1 more source

Lower central series and free resolutions of hyperplane arrangements

, 2002
If $M$ is the complement of a hyperplane arrangement, and $A=H^*(M,\k)$ is the cohomology ring of $M$ over a field of characteristic 0, then the ranks, $\phi_k$, of the lower central series quotients of $\pi_1(M)$ can be computed from the Betti numbers, $
Schenck, Henry K., Suciu, Alexander I.
core   +4 more sources

Equivariant Hilbert and Ehrhart series under translative group actions

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study representations of finite groups on Stanley–Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions allows us to use the theory of proper colorings of simplicial complexes without requiring an explicit coloring to be given.
Alessio D'Alì, Emanuele Delucchi
wiley   +1 more source