Is it always true that an element has the same order as its inverse?
5089
An element of a group has the same order as its inverse
83452
Prove that any conjugate of $a$ has the same order as $a$.
79055
Orders of a symmetric group
31113
Why is normal ordering a valid operation?
132287
Axiom of Choice and Right Inverse
16476
Order of the product of two commuting elements with coprime orders in a group.
73323
Permutations when some objects are alike
126569
Can we find a well ordering on an infinite set with no largest element?
69833
Number of elements not equal to their inverses is even number
58561
Right and left inverse
111720
Is "have the same cardinality" a equivalence relation?
108330
Product of all elements in finite abelian group equals its own inverse
74377
Is the natural order relation on an idempotent semiring total/linear?
78556
Why isn't [1,2,3] equal to itself in Javascript?
133850
Why does Mathematica order polynomial forms in reverse from traditional order?
125026
When does order of partial derivatives matter?
121423
Prove that every element of a finite group has an order