Abstract: c-Supplement is generalized and weak c-supplement is introduced.Let G be a finite group and H a subgroup of G.H is called weakly c-supplemented in G if there exists a subgroup K of G such that G=HK and H∩K≤H■,where H■ is the maximal quasinormal subgroup of G contained in H.K is called a weak c-supplement of H in G.It is shown that for the least prime divisor p of the order of a finite group G and for a Sylow p-subgroup P of G,if every 2-maximal subgroup of P is c-supplemented in G and if G is not involved with A4,then G is p-nilpotent.
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: article
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