Finite primitive permutation groups and regular cycles of their elements
Finite primitive permutation groups and regular cycles of their elements
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有限本原置换群及其元素的正则循环
DOI：
10.1016/j.jalgebra.2014.08.015
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发表时间：
2013
影响因子：
0.9
通讯作者：
Pablo Spiga
中科院分区：
文献类型：
--
作者：
Michael Giudici;C. Praeger;Pablo Spiga
我们猜想，如果G是一个有限本原群，且g是G的一个元素，则要么元素g有一个长度等于它的阶的圈，要么对于某个r，m和k，群G≤ Sym（m）wrSym（r），保持Sym（m）或Alt（m）在k-集上的自然作用的r个直接拷贝的积结构。本文将这一猜想归结为几乎单群G的基柱为经典群的情形。
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.