Self-centralizing Subgroup of Supersolvable Groups
The self-centralizing subgroup is an important subgroup which is called H as the self-centralizing subgroup of the finite group G,ifH≤G,satisfies CG(H)≤ H.When a finite group G is ap-group or a nilpotent group,its maximal abelian normal subgroup is a self-centralizing subgroup.This result can be extended to finite supersolvable groups.As an application,we calculate a self-centralizing subgroup of order 16 G=<a,b| a8=1,b2=a4,b-1ab=a-1>and give an untenable coun-terexample on a solvable group G=SL(2,3).
supersolvable groupsmaximal abelian normal subgroupsself-centralizing sub-group
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