If $G$ has inverse of all elements, then $G$ is a group. $($ true / false$) ?$
133762
A set which satisfies all conditions for a Group except associativity
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
153797
Is a quotient group a subgroup?
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
49338
Is every group a Galois group?
145406
Prove every element of $G$ has finite order.
108330
Product of all elements in finite abelian group equals its own inverse
158873
Is every group the unit group of some ring?
11825
Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \in H \iff a \in H\}$. Prove that $K$ is a subgroup of $G$.
145127
For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
126771
Group element not taken to its inverse by any automorphism
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
55976
Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
25748
If $G / Z(G)$ nilpotent then G is nilpotent.
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$