Zalygin rhymes with:
kosygin, beghin, burgin, coggin, duggin, fagin, feigin, flanagin, goggin, googin, hangin', holguin, jungin, kagin, koryagin, kosygin, mangin, melugin, mungin, muskegon, nagin, olguin, riggin, rogin, scoggin, scogin, scroggin, singin', wergin, wiggin