Divisible difference sets with multiplier -1 (Q918554)

Severe restrictions on the parameter of a divisible difference set D in an Abelian group G admitting the multiplier -1 are given, together with restrictions on the structure of G. Many series of examples (each obtained by an interesting construction) are given, also for cases in which -1 induces an automorphism of dev D without fixing any translate of D. A class of cyclic reversible divisible difference set is completely characterized. Methods are mainly algebraic, involving group rins and characters (with number-theoretical considerations). In the paper there are too many interesting results and techniques (and also enlightening recalls of previous results with new comments and applications) to permit to go here in more details.