Dinner and math.
EDIT: Here’s an interesting sidenote. If you try to generalize your approach to PMATH 346 A5P4 (e.g., try to count how many distinct isomorphism classes of finite abelian groups of order there are — for arbitrary ) then you will find it is related to the number of integer partitions of the exponents of the primes appearing in the prime factorization of .
Some random problems I thought up:
What is the automorphism group of a dihedral group? (So meta…)
Is there a group such that the sequence defined by , and for all never becomes constant?
Does there exist an infinite group , a non-trivial inner automorphism (note immediately that this means must be non-abelian if it exists), and proper infinite subgroups and so that but ?
Are there two non-isomorphic groups and with injective homomorphisms and ?
(Feel free to submit responses).