On M-Normal Subgroups in Finite Groups
Song Ying-chun
Abstract
Song Ying-chun
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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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