Let $G = {5, 15, 25, 35}$. Prove that $G$ is a group under multiplication modulo $40$. (Without using Cayley Table)
136300
{5,15,25,35} is a group under multiplication mod 40
87946
Proving that the unities of a ring form a group under multiplication
33138
Is Rational number under multiplication group?
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
11957
G is the product of its Sylow subgroups
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
95229
Qualifying Exam Question On Elementary Group Theory
133298
Assume $|G|=40$. Show that the subgroup of order $8$ is normal and unique.
92899
$G$ is non abelian simple group of order $<100$ then $G\cong A_5$
158074
Cyclic group $G$ with generator $ab$.
4048
Find the Galois group of $x^3-5$ over $\mathbb{Q}$.
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian