The modular isomorphism problem asks whether a finite 
-group is determined, up to group
isomorphism, by its group algebra over the finite field 
. The general assertion is false in characteristic
2, while the odd-characteristic problem remains open (Margolis 2022).
Tuzzolo (2026, Corollary 1.1) proves a positive answer for odd primes 
when the group has exponent 
and nilpotency class less than 
. Thus, for such a finite 
-group 
, an isomorphism 
with a finite 
-group 
forces 
. The result is a restricted positive case and does not settle
the remaining odd-characteristic problem.
