On C-section and C-index of finite groups

Research Report MRR98-013

On C-section and C-index of finite groups

Li Shirong and Yanming Wang

Abstract: Let G be a finite group and let M be a maximal subgroup of G. For each chief factor K/L of G such that $L\leq M$ and G =MK, we called the group $M \cap K/L$ a c-section of M in G. All c-sections of M are isomorphic. Using the concept of c-sections, we obtain some new characterizations of solvable and $\pi$ -solvable groups, and generalize a number of known results on the normal index and c-normal.

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