22
votes
1answer
644 views

Recovering a finite group's structure from the order of its elements.

Suppose you know the following two things about a group $G$ with $n$ elements: the order of each of the $n$ elements in $G$; $G$ is uniquely determined by the orders in (1). Question: How ...
3
votes
3answers
258 views

Is there a simple way to distinguish between group homomorphisms?

More precisely, I am given a function $f:G\to H$ with the promise that it is a homomorphism. Is there an easy way to determine which homomorphism it is without looking through all of its values? For ...