New posts in Exact Sequence

Does the short exact sequence $0\mapsto \mathbb{Z}^k\mapsto \Gamma\mapsto \mathbb{Z}^\ell\mapsto 0$ split?

The only group $G$ with one $A$ and one $B$ as composition factors is $G = A\times B$ (where $A$ and $B$ are non-abelian, finite and simple)

Torsion in abelian groups

Is $0 \to p \to R_p \to Frac(R/p) \to 0$ exact sequence?

Automorphism group of the projective unitary group PU(N) and SO(N)

What is the intuition behind short exact sequences of groups; in particular, what is the intuition behind group extensions?

Relative homology $H_n(T^2,S^1)$ (Hatcher, Exc 2.1,17.b)

Second homotopy group of real Grassmannians $\textrm{Gr}(n,m)$, special case $n=m=2$ not clear.

Dual Commutes with Base Change

What is a short exact sequence?