In  and , Sherman and Atkins, in connection with a problem in statistics, introduced a generalization of the concept of a subgroup of Z2. These generalized subgroups, which we call CWAT-sets (where "CWAT" is an acronym for "Closed With A Twist" ), have a rich algebraic structure. In this paper we establish some simple combinatorial facts about CWAT-sets, as well as provide two construction methods, prove a divisibility theorem, and make a classification conjecture.
Wattenburg, Martin, "Some Facts About CWAT-Sets" (1990). Mathematical Sciences Technical Reports (MSTR). 148.