Hi everyone. I have been getting into abstract algebra out of interest and recommendation. When I read about permutations and their cyclic decomposition from group theory perspective, I have been trying to find other objects or common problems that often come up in competitive programming and can be viewed through the lens of group theory in a different perspective. So far I have only found burnside's lemma for counting problems. I am also looking for problems that may be simplified through isomorphism or other concepts that are fundamental in group theory. The ones I did find seem to be way out of my league :(