Xiu Li
Abstract
For a maximal subgroup M of a finite group G, a θ_ subgroup C is any subgroup of G such that CM and Core α(M∩C) is maximal among normal subgroups of G properly contained in C .This paper is devoted to discussing the solvability of finite groups and some new conditions are established which insure a group to be solvable.
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For a maximal subgroup M of a finite group G, a θ_ subgroup C is any subgroup of G such that CM and Core α(M∩C) is maximal among normal subgroups of G properly contained in C .This paper is devoted to discussing the solvability of finite groups and some new conditions are established which insure a group to be solvable.
Key concepts: Mathematics, Maximal subgroup, Characteristic subgroup, Index of a subgroup, Normal subgroup, Fitting subgroup, Combinatorics, Group (periodic table)