In this paper, we prove results on the relationship between the complexity of the group and color isomorphism problems. The difficulty of color isomorphism problems is known to be closely linked to the the composition factors of the permutation group involved. Previous works are primarily concerned with applying color isomorphism to bounded degree graph isomorphism, and have therefore focused o...

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group L2(49). As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to L2(49) except L2(49) · 22. Also, we prove that if M is an almost simple group relate...

We investigate the automorphism groups of graded algebras defined by lattice polyhedral complexes and of the corresponding projective varieties, which form arrangements of projective toric varieties. These groups are polyhedral versions of the general and projective linear groups. It is shown that for wide classes of complexes they are generated by toric actions, elementary transformations and ...