True or false? $(\mathbb{Z} \setminus \left\{0\right\}, \cdot)$ is a group
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
139934
In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
23517
Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
112407
Set of left cosets is a group
92873
To prove in a Group Left identity and left inverse implies right identity and right inverse
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
40846
When can a (finite) group be written as the quotient of some other group by its center?
45508
Is the empty set a group?
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
19683
Is a semigroup $G$ with left identity and right inverses a group?
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
19822
For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?