The Depth of Subgroups of Suzuki Groups

Abstract

We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others, the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.

Key Words:

• Combinatorial depth
• Ordinary depth
• Simple Suzuki group
• Subgroup

2010 Mathematics Subject Classification:

• 20B20
• 20C33
• 20C15

ACKNOWLEDGMENTS

The authors thank Thomas Breuer for several useful suggestions and comments.

Notes

Communicated by A. Turull