Show that the orders of $x$ and $axa^{−1}$ of a group are equal
83452
Prove that any conjugate of $a$ has the same order as $a$.
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
41731
Question about the order of the product of two elements in an abelian group
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
79055
Orders of a symmetric group
88344
Order of a group and subsequent subgroups
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
21217
$G$, group. $a,b\in G$. Show that $|a|=|a^{-1}|; |ab|=|ba|$, and $|a|=|cac^{-1}|, \forall c\in G$.
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
68971
Elementary approach to proving that a group of order 9 is Abelian
83710
Order of a homomorphism of groups
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
63499
Groups of prime squared order
102634
Order of the Rubik's cube group
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
157582
Inverse of $ab$ and its order in a group with relations $a^2=e=b^6$ and $ab=b^4a$
83654
Order of an element in a finite cyclic group