Is it a variant of Strong RSA assumption?
The modulus $N$ is implicit in the group $\mathbb Z_N^\ast$ that $c$ and $g$ are chosen from. That is, in this context, $g^a$ is taken to mean "the residue class represented by $x^a\bmod N$ where $x$ denotes some representant of $g$'s residue class".

Therefore, when additionally requiring that $a\geq3$ and odd, this notion is equivalent to the strong RSA assumption as defined in Rivest's paper.