Proving this non-empty set and binary operation is a group
14097
A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
90590
Prove that the following set is dense
96202
Prove composition of bijections is bijection
112407
Set of left cosets is a group
30136
Proof that a Combination is an integer
70164
Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
26572
Does the Symmetric difference operator define a group on the powerset of a set?
73056
Operation that makes the negative real numbers, $\mathbb{R}_{<0}$, a group
26569
Counting binary operations on a set with $n$ elements
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
5089
An element of a group has the same order as its inverse
122048
why is the set of all binary sequences not countable?
18308
Coset multiplication giving a well defined binary operation
61602
Binary strings (words) proof
98355
Is the set of all possible binary strings countable?
118022
Show that a group of order $180$ is not simple.
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$