Is $(\mathbb{R},*)$, where $a*b=ab+a+b$, a group?
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
125345
Suppose $a$ and $b$ are group elements, $a$ and $b$ commute, $|a|$ and $|b|$ are both finite. What are the possibilities for $|ab|$?
158873
Is every group the unit group of some ring?
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
72507
Does $ab=1$ imply $ba=1$ in a ring?
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
85913
R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following
78006
What is known about the quotient group $\mathbb{R} / \mathbb{Q}$?
48211
When is $(a+b)^n \equiv a^n+b^n$?
102299
Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
93776
Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
61375
Meaning of $\mathbb{R}[x]$
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
89192
$(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$