The Minimal Number of Cyclic Generators of the Symmetric and Alternating Groups

Abstract

The aim of this note is to find the minimal number of generators of the symmetric group S _n and alternating group A _n , when the generators are cycles of length at most k. The approach is constructive.

Key Words:

• Alternating group
• Cycles
• Generators
• Symmetric group

ACKNOWLEDGMENT

The author is grateful to Anna Melnikov for suggesting the problem and to Moshe Roitman for useful discussions.

Notes

Communicated by A. Yu. Olshanskii.