Using a result of de Smit and Lenstra, we prove that the order of a group containing nontrivial Gassmann equivalent subgroups must be divisible by at least five primes, not necessarily distinct. We then investigate the existence of Gassmann equivalent subgroups in groups with order divisible by exactly five primes.

Author Bio

I am currently a senior at Wheaton College just outside Chicago, Illinois. I plan to attend graduate school in mathematics and pursue a PhD. I wrote "On the Order of a Group Containing Nontrivial Gassmann Equivalent Subgroups" for the REU at Louisiana State University over the summer of 2008.