A Solution to a Problem of Wiegold

Abstract

It is well known that a non-abelian finite simple group G can be generated by two elements, i.e., it is 2-generated. We show that the direct product of n copies of G is 2-generated, where n is the smallest integer larger than . This answers a question of Wiegold.

Key Words:

• Finite simple group
• Generation

2000 Mathematics Subject Classification:

• Primary 20B30
• Secondary 20P05

ACKNOWLEDGMENTS

The research of the first author was mainly supported by a grant from INDAM-GNSAGA, and partly by a Marie Curie International Reintegration Grant within the 7th European Community Framework Programme, by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by OTKA K84233.

Notes

Communicated by P. Tiep.