Group Theory Problem Solver

I’m working through a set of graduate-level questions in pure mathematics and need solid, reliable help specifically in Abstract Algebra—more precisely, Group Theory. The tasks range from constructing rigorous proofs to clarifying tricky concepts like normal subgroups, homomorphisms, Sylow theorems, and group actions.

What I’m looking for is clear written explanations (LaTeX-ready), step-by-step reasoning that I can follow and reference later, and the occasional live walkthrough when a problem calls for deeper discussion. If you are comfortable juggling definitions, theorems, and counter-examples in this area, I’d love your support so I can submit polished, well-argued solutions with confidence.