of p, including 1, there exists a pgroup whose conjugacy class sizes are exactly the members of S. The groups constructed by Cossey and Hawkes are of nilpotency class 2.Conjugacy classes in extra special groups. By definition, an extraspecial group is a nonabelian group such that is cyclic of order and is an elementary abelian group. I read somewhere that obviously the conjugacy class sizes of such a group is and I was trying to prove this fact. To prove this, conjugacy classes of p-groups

Conjugacy classes of the Ree groups. Consider the finite simple Ree groups where is a positive integer. I would like to know the orders of conjugacy class representatives of and from there to know the number of conjugacy classes of singular elements of (an element is 3singular if its order is divisible by 3).

Conjugacy classes of a pgroup. For a p group of order p4, assume the center of G has order p2. Determine the number of conjugacy classes of G. What I have tried: each element of the center constitutes a conjugacy class; the other conjugacy classes have order a power of p; their sum is p4p2.

Let K be a conjugacy class of a finite pgroup G where p is a prime, and let K 1 denote the conjugacy class of G consisting of the inverses of the elements in K.

Rating: 4.71 / Views: 606Abstract. In this paper we provide examples of pairs of but topologically equivalent, p groups H 1; H 2 Aut( S ), where S is a closed Riemann surface of genus g 2, so that SH j hasgenus zero and all its cone points are of order equal to p. 1. IntroductionWe denote by Aut( S ) the group of conformal automorphisms of a Riemannsurface S.

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