2002Natural Science Journal of Xiangtan UniversityRequires access

On M-Normal Subgroups in Finite Groups

Song Ying-chun

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Abstract

with the concept of mnormal subgroups,this paper gives some result about msubgroups: 1.When all sylow subgroups about G is mnormal subgroups,and there is a sylow subgroups which is normal subgroup,finite group G is a solvable group. 2.When all sylow subgroups about G is mnormal subgroups,there is a sylow subgroups which is normal subgroup,and |G|=p α 1 1p α 2 2...p α n n,(n≥3),finite group G is a nilpotent group.

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What this paper is about

with the concept of mnormal subgroups,this paper gives some result about msubgroups: 1.When all sylow subgroups about G is mnormal subgroups,and there is a sylow subgroups which is normal subgroup,finite group G is a solvable group. 2.When all sylow subgroups about G is mnormal subgroups,there is a sylow subgroups which is normal subgroup,and |G|=p α 1 1p α 2 2...p α n n,(n≥3),finite group G is a nilpotent group.

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Available abstract

with the concept of mnormal subgroups,this paper gives some result about msubgroups: 1.When all sylow subgroups about G is mnormal subgroups,and there is a sylow subgroups which is normal subgroup,finite group G is a solvable group. 2.When all sylow subgroups about G is mnormal subgroups,there is a sylow subgroups which is normal subgroup,and |G|=p α 1 1p α 2 2...p α n n,(n≥3),finite group G is a nilpotent group.

Key concepts: Sylow theorems, Locally finite group, Mathematics, Normal subgroup, Complement (music), Finite group, p-group, Fitting subgroup

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