What kind of programs there are for a math student to solve problems and prove theorems related to abstract algebra?
SageMath is an open-source mathematics software system that integrates various mathematical software packages. It includes functionality for algebraic computations, group theory, ring theory, and other topics in abstract algebra.
Isabelle/HOL is another interactive theorem prover that supports higher-order logic. It provides a framework for constructing formal proofs and conducting mathematical reasoning. It is used in formal verification and can be utilized to prove theorems related to abstract algebra.