Abstract
If is embedded as a proper subgroup ofX in the Cayley representation of G, then the problem of if Nx(G) is always larger than G is studied in this paper.
Highlights
If 17 is abelian 17 is self centralizing in Sn
The normalizer of 17 in Sn is equal to 17- Aut(17) where Aut(17) is the full automorphism group of 17
That X must contain an element of the outer automorphism group of 17
Summary
If 17 is abelian 17 is self centralizing in Sn. the normalizer of 17 in Sn is equal to 17- Aut(17) where Aut(17) is the full automorphism group of 17 (see Lemma 2). > Bhattacharya 1] proved that if 17 is any finite, abelian p group satisfying (*) Nx(17) 17. In this paper we will igrove that if 17 is any abelian Hall subgroup of X, satisfying the condition We will give an example to show that the condition of being Hall subgroup is necessary in the above theorem.
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