Newbetuts

Prove that the augmentation ideal in the group ring $\mathbb{Z}/p\mathbb{Z}G$ is a nilpotent ideal ($p$ is a prime, $G$ is a $p$-group)

Semidirect product: general automorphism always results in a conjugation

Tensor Products and Von Neumann's Direct Multiplication

Let $f: (\Bbb Z_{28}, +)\to(\Bbb Z_{16}, +)$ be a group homomorphism such that $f(1)=12$. Find $\ker f$.

Characterize the commutative rings with trivial group of units

If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.

$\mathrm{Aut}(\mathrm{Aut}(G))\cong\mathrm{Aut}(G)$ for $G$ a non-abelian simple group

Show that a group of order $pq$ has subgroup of order $p$ and $q$ without using sylow's and cauchy's theorem

Solvable group of order $pqr^2$

free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$

question regarding Jacobi's identity [duplicate]

Center of Weyl algebra over a field of characterstic $0$?

Why is the absence of zero divisors not sufficient for a field of fractions to exist?

Tensor products commute with inductive limit

New posts in abstract-algebra

If N and every subgroup of N is normal in G then G/N is abelian .

Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)

Intersection of field extensions

Proving (without using complex numbers) that a real polynomial has a quadratic factor

Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$. [duplicate]

The unique loop (quasigroup with unit) $L$ of order $5$ satisfying $x^2 = 1$ for all $x \in L$

Prove that the augmentation ideal in the group ring $\mathbb{Z}/p\mathbb{Z}G$ is a nilpotent ideal ($p$ is a prime, $G$ is a $p$-group)

Semidirect product: general automorphism always results in a conjugation

Tensor Products and Von Neumann's Direct Multiplication

Let $f: (\Bbb Z_{28}, +)\to(\Bbb Z_{16}, +)$ be a group homomorphism such that $f(1)=12$. Find $\ker f$.

Characterize the commutative rings with trivial group of units

If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.

$\mathrm{Aut}(\mathrm{Aut}(G))\cong\mathrm{Aut}(G)$ for $G$ a non-abelian simple group

Show that a group of order $pq$ has subgroup of order $p$ and $q$ without using sylow's and cauchy's theorem

Solvable group of order $pqr^2$

free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$

question regarding Jacobi's identity [duplicate]

Center of Weyl algebra over a field of characterstic $0$?

Why is the absence of zero divisors not sufficient for a field of fractions to exist?

Tensor products commute with inductive limit