Nowadays many hundreds of methods are practised; all, in some degree, owe a debt to Stedman's pioneering work which has value as well in mathematics (group theory) as well as the more limited field of bell-ringing.
Prof. Passi is a noted group-theorist in India, has made significant contribution to certain aspects of theory of groups specially to the study of group rings.
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In 1898 George Miller delineated the structure of a Hamiltonian group in terms of its order and that of its subgroups.
Howard Hawks Mitchell (January 13, 1885, Marietta, Ohio – 1943) was an American mathematician who worked on group theory and number theory and who introduced Mitchell's group.
This is a powerful application of group theory to vibrational spectroscopy, and allows one to easily detect the presence of this symmetry element by comparison of the IR and Raman spectra generated by the same molecule.
Dirichlet does not explicitly recognise the concept of the group that is central to modern algebra, but many of his proofs show an implicit understanding of group theory.
See the books by Irving Kaplansky, László Fuchs, Phillip Griffith, and David Arnold, as well as the proceedings of the conferences on Abelian Group Theory published in Lecture Notes in Mathematics for more recent results.
The central part of Burnside's group theory work was in the area of group representations, where he helped to develop some of the foundational theory, complementing, and sometimes competing with, the work of Ferdinand Frobenius, who began his research in the subject during the 1890s.
Predrag Cvitanović, Group Theory: Birdtracks, Lie's, and Exceptional Groups.