Quotients and invariants of $$\mathcal {AS}$$-sets equipped with a finite group action
Sign Up to like & getrecommendations! Published in 2020 at "Mathematische Annalen"
DOI: 10.1007/s00208-020-01994-7
Abstract: Using the geometric quotient of a real algebraic set by the action of a finite group G, we construct invariants of G-affine real algebraic varieties with respect to equivariant homeomorphisms with algebraic graph, including additive… read more here.
Keywords: quotients invariants; mathcal sets; finite group; invariants mathcal ... See more keywords
Conjugacy of Maximal and Submaximal ????-Subgroups
Sign Up to like & getrecommendations! Published in 2018 at "Algebra and Logic"
DOI: 10.1007/s10469-018-9490-9
Abstract: Let ???? be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Following H. Wielandt, we call a subgroup H of a finite group G a submaximal ????-subgroup if there exists… read more here.
Keywords: conjugacy maximal; subgroup; submaximal subgroups; group ... See more keywords
On the Solvability of a Finite Group with S-Seminormal Schmidt Subgroups
Sign Up to like & getrecommendations! Published in 2019 at "Ukrainian Mathematical Journal"
DOI: 10.1007/s11253-019-01603-0
Abstract: A finite nonnilpotent group is called a Schmidt group if all its proper subgroups are nilpotent. A subgroup A is called S-seminormal (or SS-permutable) in a finite group G if there is a subgroup B… read more here.
Keywords: schmidt subgroups; solvability finite; group; finite group ... See more keywords
On the order supergraph of the power graph of a finite group
Sign Up to like & getrecommendations! Published in 2020 at "Ricerche di Matematica"
DOI: 10.1007/s11587-020-00520-w
Abstract: The power graph $${\mathcal {P}}_{G}$$ P G of a finite group G is the graph whose vertex set is G , two distinct vertices are adjacent if one is a power of the other. The… read more here.
Keywords: order supergraph; power; graph; finite group ... See more keywords
The block graph of a finite group
Sign Up to like & getrecommendations! Published in 2021 at "Israel Journal of Mathematics"
DOI: 10.1007/s11856-021-2192-3
Abstract: This paper studies intersections of principal blocks of a finite group with respect to different primes. We first define the block graph of a finite group $G$, whose vertices are the prime divisors of $|G|$… read more here.
Keywords: block graph; graph finite; group; finite group ... See more keywords
On the number of simple modules in a block of a finite group
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2016.10.022
Abstract: Abstract We prove that if B is a p-block with non-trivial defect group D of a finite p-solvable group G, then l ( B ) p r , where r is the sectional rank of… read more here.
Keywords: number simple; modules block; group; finite group ... See more keywords
Multiple holomorphs of finite p-groups of class two
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2018.09.031
Abstract: Abstract Let G be a group, and S ( G ) be the group of permutations on the set G. The (abstract) holomorph of G is the natural semidirect product Aut ( G ) G… read more here.
Keywords: non abelian; class; hol; multiple holomorphs ... See more keywords
Construction of the irreducible modular representations of a finite group
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2019.08.015
Abstract: Abstract A complete procedure is described for constructing the irreducible KG-modules and their Brauer characters, where K is a finite field of characteristic p and G is a finite permutation or matrix group. The central… read more here.
Keywords: construction irreducible; modular representations; finite group; representations finite ... See more keywords
The prime graph on class sizes of a finite group has a bipartite complement
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2019.09.022
Abstract: Abstract Let G be a finite group, and let cs ( G ) denote the set of sizes of the conjugacy classes of G. The prime graph built on cs ( G ) , that… read more here.
Keywords: prime graph; graph; finite group; graph class ... See more keywords
On sheaves in finite group representations
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2022.107085
Abstract: Given a general finite group $G$, we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. We give an intrinsic new proof to the equivalence of M. Artin between the category… read more here.
Keywords: finite group; group; group representations; sheaves finite ... See more keywords
Autocommuting probability of a finite group
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Algebra"
DOI: 10.1080/00927872.2017.1332201
Abstract: ABSTRACT Let G be a finite group and Aut(G) the automorphism group of G. The autocommuting probability of G, denoted by Pr(G,Aut(G)), is the probability that a randomly chosen automorphism of G fixes a randomly… read more here.
Keywords: autocommuting probability; probability; group autocommuting; finite group ... See more keywords