Show that elements are not conjugate to their inverse in groups of odd order.
116737
An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
1577
Order of nontrivial elements is 2 implies Abelian group
127664
Inverse elements in the absence of identities/associativity.
75473
If a group $G$ has odd order, then the square function is injective.
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
26398
Group of even order contains an element of order 2
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
113413
How do I show that two groups are not isomorphic?
102622
K is a subgroup of G. Show that K is not a normal subgroup
27780
Subgroup which is generated by odd elements
141922
Reason for reversing the order when transpose and inverse of a group of matrices
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
56607
gcd and order of elements of group
2731
Groups of even order have an element whose order is 2.
83654
Order of an element in a finite cyclic group
157582
Inverse of $ab$ and its order in a group with relations $a^2=e=b^6$ and $ab=b^4a$