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
A semidirect product G=F⋋H of groups F and H is called a Frobenius group if the following two conditions are satisfied:(F1)H acts freely on F,that is,fh=f for f in F and h in H only if^(h)=1 or f=1.(F2)Every non-ident...A semidirect product G=F⋋H of groups F and H is called a Frobenius group if the following two conditions are satisfied:(F1)H acts freely on F,that is,fh=f for f in F and h in H only if^(h)=1 or f=1.(F2)Every non-identity element h∈H of finite order n induces in F by conjugation in G a splitting automorphism,that is,ff^(h)⋯fh^(n−1)=1 for every f∈F;in other words,the order of f^(h−1)is equal to n.We describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.展开更多
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.
基金The work was supported by the Program of Fundamental Research of the SB RAS no.1.1.1(project no.0314-2019-0001).
文摘A semidirect product G=F⋋H of groups F and H is called a Frobenius group if the following two conditions are satisfied:(F1)H acts freely on F,that is,fh=f for f in F and h in H only if^(h)=1 or f=1.(F2)Every non-identity element h∈H of finite order n induces in F by conjugation in G a splitting automorphism,that is,ff^(h)⋯fh^(n−1)=1 for every f∈F;in other words,the order of f^(h−1)is equal to n.We describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.
