Problem of Algebra Abstract by Herstein sec. 2.2 number 4
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
23077
Prove that the dihedral group $D_4$ can not be written as a direct product of two groups
4228
Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
119758
On the order of elements of $\mathrm{GL}(2,q)$.
148310
Showing rational numbers are algebraic
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
78564
Prove: $D_{8n} \not\cong D_{4n} \times Z_2$.
144250
subideals of an ideal
46687
Elements of $GL_{2}(\mathbb{Z})$ of finite order
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
48804
Enumeration of rationals from Stein-Shakarchi's Real Analysis (Chapter 1, Exercise 24)
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
45627
Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
31585
Primary ideals of $\mathbb{Z}$