For a p-block B of a finite group G, we give a bound of the order of its defect group D in terms of k(B), the number of the irreducible ordinary characters in B.
Let G be a finite group. For k ∈ N, X ∈ Irr（G）, define c（k）x ：= 1/G ∑g∈G x（gk）. This is called the k-th Frobenius-Schur indicator of X. In this article we study the Probenius-Schur indicators for Frobenius ...Let G be a finite group. For k ∈ N, X ∈ Irr（G）, define c（k）x ：= 1/G ∑g∈G x（gk）. This is called the k-th Frobenius-Schur indicator of X. In this article we study the Probenius-Schur indicators for Frobenius groups, p-groups, semidihedral groups and mod- ular p-groups. Further, we use this to study the function ζ kG（g） which counts the number of roots of xk = g in a finite group G.展开更多
基金the National Natural Science Foundation of China (Grant No. 10071061) Fujian Province Science Foundation and Mathematical Center of Ministry of Education of China.
文摘For a p-block B of a finite group G, we give a bound of the order of its defect group D in terms of k(B), the number of the irreducible ordinary characters in B.
文摘Let G be a finite group. For k ∈ N, X ∈ Irr（G）, define c（k）x ：= 1/G ∑g∈G x（gk）. This is called the k-th Frobenius-Schur indicator of X. In this article we study the Probenius-Schur indicators for Frobenius groups, p-groups, semidihedral groups and mod- ular p-groups. Further, we use this to study the function ζ kG（g） which counts the number of roots of xk = g in a finite group G.
