arXiv subjects

Kyle Rosa

Publications and source records attributed to Kyle Rosa.

2 recordsLinked to original sources

arXiv2018

Bounds for Finite Semiprimitive Permutation Groups: Order, Base Size, and Minimal Degree

In this paper we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size, minimal degree, fixity, and chief length of an arbitrary finite semiprimitive group in terms of its degree. To establish these bounds, we classify finite semiprimitive groups that induce the alternating or symmetric group on the set of orbits of an intransitive normal subgroup.

math.GR↗

arXiv2018

Bounding the composition length of primitive permutation groups and completely reducible linear groups

We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds on the composition length of a finite completely reducible linear group in terms of some of its parameters. In almost all cases we show that the bounds are sharp, and describe the extremal examples.

math.GR↗