Any compact connected Lie group has Euler characteristic zero. What are the possible values for the Euler characteristic of a connected, but not necessarily compact Lie group?
Any field that is finitely generated as a ring is a finite field.
Given a group , embed in a larger group such that any automorphism of is the restriction of an inner automorphism of .
Is there a bijection of the plane sending every circle to a square?
Exhibit a group , a set of generators for and a subgroup such that for all and yet is not normal in .
What is the number of idempotent functions ?
Is there a ring such that there are two different ring injections ?