ON FINITE GROUPS WITH SPECIFIC NUMBER OF CENTRALIZERS

Authors : Sekhar Jyoti BAİSHYA

Pages : 53-62

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Publication Date : 2013-06-01

Article Type : Research Paper

Abstract :For a group G, | Centinsert ignore into journalissuearticles values(G); | denotes the number of distinct centralizers of its elements. A group G is called n-centralizer if | Centinsert ignore into journalissuearticles values(G); |= n, and primitive n-centralizer if | Centinsert ignore into journalissuearticles values(G); |=| Centinsert ignore into journalissuearticles values(GZinsert ignore into journalissuearticles values(G);); |= n. In this paper, among other things, we investigate the structure of finite groups of odd order with | Centinsert ignore into journalissuearticles values(G); |= 9 and prove that if |G| is odd, then | Centinsert ignore into journalissuearticles values(G); |= 9 if and only if GZinsert ignore into journalissuearticles values(G);∼= C7 o C3 or C7 × C7.
Keywords : finite group, n centralizer group, primitive n centralizer group