# Is finite abelian group isomorphism in Log Space?

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 [1].

Question : Is this problem known to be in Log Space?

I tried to google but did not get anything related to log space.

[1] T. Kavitha, Linear time algorithms for Abelian group isomorphism and related problems. Journal of Computer and System Sciences 73(6):986–996. (Science Direct)

The finite abelian group-isomorphism when groups are given in the form of multiplication tables known to be in $L$ and in $TC^0 (FOLL)$. For more detail you can see the thesis of the Dr. Fabian.

PhD Thesis of Dr. Fabian ( see page number 180 and 185 )