7.2. Resources¶
7.2.1. Online proofs¶
Theorem
If every element of a group is its self inverse, then that group is abelian.
Theorem
If all elements of a group G (except e) have order 2, then G is abelian.
Theorem
Every group of prime order is cyclic.
http://planetmath.org/ProofThatEveryGroupOfPrimeOrderIsCyclic.html
Proposition
A group of even order has a non-identity element which is its own inverse. Or a group of even order contains an element of order 2.
http://planetmath.org/AGroupOfEvenOrderContainsAnElementOfOrder2.html