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2011•Basic Sciences Journal of Textile UniversitiesRequires access

The finite Abelian groups with automorphism groups of degree 2~6p~2

Xiaowei Pan

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Abstract

Let p be an odd prime,let G be a finite Abelian group,and let A(G) denotes the automorphism group of G.In this paper,using method of elementary number theory,it is proved that if |A(G)|=26p2,where p≠ 3,5 or 17,then G has at most 20 types.

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Let p be an odd prime,let G be a finite Abelian group,and let A(G) denotes the automorphism group of G.In this paper,using method of elementary number theory,it is proved that if |A(G)|=26p2,where p≠ 3,5 or 17,then G has at most 20 types.

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Available abstract

Let p be an odd prime,let G be a finite Abelian group,and let A(G) denotes the automorphism group of G.In this paper,using method of elementary number theory,it is proved that if |A(G)|=26p2,where p≠ 3,5 or 17,then G has at most 20 types.

Key concepts: Mathematics, Abelian group, Automorphism, Inner automorphism, Prime (order theory), p-group, Pure mathematics, Combinatorics

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