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2009•Journal of Qufu Normal UniversityRequires access

Some Sufficient Conditions for Solvability of Finite Groups

Rui Xue

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Abstract

A subgroup H of a finite group G is said to be weakly c-normal in G if there exists a subnormal subgroup K of G such that G=HK and H∩K≤ HG,where HG is the maximal normal subgroup of G that is contained in H.The researchon weakly c-normal subgroups has been Proposed by many Scholars for a long time,and the research in this field is still very active. Using weakly c-normal subgroups,some sufficient conditions for solvability of finite groups are obstained.

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What this paper is about

A subgroup H of a finite group G is said to be weakly c-normal in G if there exists a subnormal subgroup K of G such that G=HK and H∩K≤ HG,where HG is the maximal normal subgroup of G that is contained in H.The researchon weakly c-normal subgroups has been Proposed by many Scholars for a long time,and the research in this field is still very active. Using weakly c-normal subgroups,some sufficient conditions for solvability of finite groups are obstained.

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Available abstract

A subgroup H of a finite group G is said to be weakly c-normal in G if there exists a subnormal subgroup K of G such that G=HK and H∩K≤ HG,where HG is the maximal normal subgroup of G that is contained in H.The researchon weakly c-normal subgroups has been Proposed by many Scholars for a long time,and the research in this field is still very active. Using weakly c-normal subgroups,some sufficient conditions for solvability of finite groups are obstained.

Key concepts: Mathematics, Normal subgroup, Combinatorics, Finite group, Fitting subgroup, Subgroup, Group (periodic table), Maximal subgroup

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