ON THE SET OF SAME-SIZE CONJUGATE CLASSES

Author (s) : D.KANTHAKUMAR, R.SATHYA SHANTHI

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Abstract :
Let G be a finite group with conjugate classes of size ni-1<B <n. Then the vector (n.nz.....n.) is said to be a group of type (n,n2n). It is well-known that there is a strong relation between the structure of a group and the sizes of its conjugate classes and there exist many results studying the structure of a group under some arithmetical conditions on its conjugate class sizes, for instance [1, 3]. Here, the structure of a group under an equivalence relation that is defined by its conjugate class sizes and we focus on the set of sizes of the equivalence classes with respect to this relation. We define an equivalence relation - on G as follows: g.h EG g-h19° | = |A| . If the conjugate type of G is V(G) (nn), then the equivalence classes of-are (x E G/Ix-n), for i E (1,2,...). In this paper, our goal is to show that simple linear groups PSL (3) and PSL2 (q), where q € (5,7,8,9,17), can be characterized by their same- size conjugate sets.

Keywords : conjugate classes.

Conference Date : 13/11/2020

Pages : 296

Paper ID : 20296