Finite primitive permutation groups and regular cycles of their elements

作者：Giudici Michael; Praeger Cheryl E^*; Spiga Pablo

来源：Journal of Algebra, 2015, 421: 27-55.

DOI：10.1016/j.jalgebra.2014.08.015

• Cycle lengths
• Element orders
• Primitive groups
• Quasiprimitive groups

We conjecture that if G is a finite primitive group and if g is an element of G, then either the element g has a cycle of length equal to its order, or for some r, m and k, the group G <= Sym(m) wr Sym(r), preserving a product structure of r direct copies of the natural action of Sym(m) or Alt(m) on k-sets. In this paper we reduce this conjecture to the case that G is an almost simple group with socle a classical group.

• 出版日期2015-1-1