A super-Brauer character theory of a group G and a prime p is a pair consisting of a partition of the irreducible p-Brauer characters and a partition of the p-regular elements of G that satisfy certain properties.We c...A super-Brauer character theory of a group G and a prime p is a pair consisting of a partition of the irreducible p-Brauer characters and a partition of the p-regular elements of G that satisfy certain properties.We classify the groups and primes that have exactly one super-Brauer character theory.We discuss the groups with exactly two super-Brauer character theories.展开更多
Let G be a finite group,p be a prime divisor of|G|,and P be a Sylow p-subgroup of G.We prove that P is normal in a solvable group G if|G:kerφ|_(p′)=φ(1)_(p′)for every nonlinear irreducible monomial p-Brauer charac...Let G be a finite group,p be a prime divisor of|G|,and P be a Sylow p-subgroup of G.We prove that P is normal in a solvable group G if|G:kerφ|_(p′)=φ(1)_(p′)for every nonlinear irreducible monomial p-Brauer characterφof G,where kerφis the kernel ofφandφ(1)_(p′)is the p′-part ofφ(1).展开更多
Let N be a normal subgroup of a finite group G.Let be an irreducible Brauer character of N.Assume π is a set of primes and (1)/(1)is a π'-number for any. X ∈IBr_p(G|).If p|G:N|, and N is p-solvable,then G/N ha...Let N be a normal subgroup of a finite group G.Let be an irreducible Brauer character of N.Assume π is a set of primes and (1)/(1)is a π'-number for any. X ∈IBr_p(G|).If p|G:N|, and N is p-solvable,then G/N has an abelian-by-metabelian Hall-π subgroup:If pπ,then G/N has a metabelian Hall-π subgroup.展开更多
For a group G,we produce upper and lower bounds for the sum of the entries of the Brauer character table of G and the projective indecomposable character table of G.When G is aπ-separable group,we show that the sum o...For a group G,we produce upper and lower bounds for the sum of the entries of the Brauer character table of G and the projective indecomposable character table of G.When G is aπ-separable group,we show that the sum of the entries in the table of Isaacs'partial characters is a real number,and we obtain upper and lower bounds for this sum.展开更多
基金supported by China Scholarship Councilthe Fund for Young Key Teachers of Henan University of Technology+2 种基金the Fund of Henan Administration of Foreign Experts Affairsthe Project of Henan Province(Grant No.182102410049)the NSFC(Grant Nos.11571129,11771356,11971189 and 11926330)。
文摘A super-Brauer character theory of a group G and a prime p is a pair consisting of a partition of the irreducible p-Brauer characters and a partition of the p-regular elements of G that satisfy certain properties.We classify the groups and primes that have exactly one super-Brauer character theory.We discuss the groups with exactly two super-Brauer character theories.
基金supported by the Cultivation Programme for Young Backbone Teachers in Henan University of Technology,the Fund of Jiangsu Province(Grant Nos.2018k099B,BK20181451)the National Natural Science Foundation of China(Grant Nos.11926330,11926326,11971189,11771356,11871062,12011530061).
文摘Let G be a finite group,p be a prime divisor of|G|,and P be a Sylow p-subgroup of G.We prove that P is normal in a solvable group G if|G:kerφ|_(p′)=φ(1)_(p′)for every nonlinear irreducible monomial p-Brauer characterφof G,where kerφis the kernel ofφandφ(1)_(p′)is the p′-part ofφ(1).
基金Supported by Beijing Natural Science Foundation[19920003]
文摘Let N be a normal subgroup of a finite group G.Let be an irreducible Brauer character of N.Assume π is a set of primes and (1)/(1)is a π'-number for any. X ∈IBr_p(G|).If p|G:N|, and N is p-solvable,then G/N has an abelian-by-metabelian Hall-π subgroup:If pπ,then G/N has a metabelian Hall-π subgroup.
基金support of the China Scholarship Council,the Cultivation Programme for Young Backbone Teachers in Henan University of Technology,and the NSFC(11926330,11926326,11971189,11771356).
文摘For a group G,we produce upper and lower bounds for the sum of the entries of the Brauer character table of G and the projective indecomposable character table of G.When G is aπ-separable group,we show that the sum of the entries in the table of Isaacs'partial characters is a real number,and we obtain upper and lower bounds for this sum.
