Das, BireswarBireswarDasSharma, ShivduttShivduttSharma2025-08-312025-08-312019-01-01[9783030199548]10.1007/978-3-030-19955-5_82-s2.0-85068604956https://d8.irins.org/handle/IITG2025/23382The isomorphism problem for groups, when the groups are given by their Cayley tables is a well-studied problem. This problem has been studied for various restricted classes of groups. Kavitha gave a linear time isomorphism algorithm for abelian groups (JCSS 2007). Although there are isomorphism algorithms for certain nonabelian group classes, the complexities of those algorithms are usually super-linear. In this paper, we design linear and nearly linear time isomorphism algorithms for some nonabelian groups. More precisely, We design a linear time algorithm to factor Hamiltonian groups. This allows us to obtain an O(n) algorithm for the isomorphism problem of Hamiltonian groups, where n is the order of the groups.We design a nearly linear time algorithm to find a maximal abelian factor of an input group. As a byproduct we obtain an O~ (n) isomorphism for groups that can be decomposed as a direct product of a nonabelian group of bounded order and an abelian group, where n is the order of the groups.falseConference Paper1611334980-9220196cpBook Series4