Exponent preserving subgroups of the finite simple groups

ABSTRACT

Given a group G denote with exp(G) its exponent, which is the least common multiple of the order of its elements. In this paper, we solve the problem of finding the finite simple groups having a proper subgroup with the same exponent. For each G with this property we will provide an explicit example of H<G with exp(G) = exp(H).

KEYWORDS:

• Exponent
• finite simple groups
• sylow subgroups

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20E07
• 20D05

Acknowledgments

I would like to thank my supervisor, Professor Andrea Lucchini, who suggested this topic for my master thesis and helped me finding some key references.