Definition : An abelian group is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written
Input : Two finite abelian groups $|G| =n$ and $|H|=n$ by their table representation
Find : Is $G \cong H$?
There is an $O(n)$ running time algorithm for this problem, due to Kavitha .
Question : Is this problem known to be in Log Space?
I tried to google but did not get anything related to log space.
 T. Kavitha, Linear time algorithms for Abelian group isomorphism and related problems. Journal of Computer and System Sciences 73(6):986–996. (Science Direct)