Conjugacy Classes ofP-Cycles of Type D in Alternating Groups

Abstract

We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in [3]. Also we determine all the subracks of those conjugacy classes which are not of type D.

Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups

“…In this series we investigate the applicability of these criteria for finite simple groups of Lie type, excluding the Suzuki and Ree groups treated in [9]. For alternating and sporadic groups, see [6,7,11,12]. Let G be a finite simple Chevalley or Steinberg group defined over a finite field F q where q = p m , with m ∈ N and p prime.…”

Finite-Dimensional Pointed Hopf Algebras Over Finite Simple Groups of Lie Type IV. Unipotent Classes in Chevalley and Steinberg Groups

“…In this series we investigate the validity of these criteria for finite simple groups of Lie type; for work on alternating and sporadic groups, see [AFGV1,F,AFGV2,FaV]. Let G be a finite simple Chevalley or Steinberg group defined over a finite field F q where q = p m , with m ∈ N and p prime.…”

Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSL(q) and PSp2(q)

“…It is natural, and convenient, to start addressing Questions 1 and 2 by assuming that G is simple non-abelian, see [9] for the importance of this reduction. When G is alternating or sporadic, this was addressed in [7,8,14,15]. The series of papers [1,2,3,4,5,12] treat the case when G is simple of Lie type.…”