On self-normality and abnormality in the alternating group Ap
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An old problem proposed by Huppert, Doerk and Hawkes motivates us to investigate the relationship between an abnormal subgroup and self-normalizing in non-solvable groups. A subgroup H of a group G is called second maximal if H is maximal in all maximal subgroups of G containing H. Our result is that if H is a second maximal subgroup of the alternating group Ap of prime degree, then H is abnormal in Ap if and only if H is self-normalizing.
KeywordsMaximal Subgroup Prime Degree Abnormal Subgroup
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