I want to work with group algebras in SageMath. But they do not behave as they should. Is this a bug or do I do something wrong? For my application, I need to work with a group defined by a presentation (the bug does not appear with permutation groups). So the simplest example should be $\mathbb{F}_2[C_2]$, with $C_2 = \langle X : X^2 = 1\rangle$.
sage: F.<X> = FreeGroup(1)
sage: G = F / [X^2]
sage: display(G)
Finitely presented group < X | X^2 >
sage: A = G.algebra(GF(2))
sage: x = A.gen()
sage: x^2 == A.one()
False
It seems that the relations of $G$ will not be presented in $R[G]$. Why?