A Steiner 2-design is 1-rotational over a group G if it admits G as an auto
morphism group fixing one point and acting regularly on the remainder, 1-ro
tational Steiner 2-designs have come into fashion since 1981, when Phelps a
nd Rosa (Discrete Math. 33 (1981), 57-66) studied Steiner triple systems th
at are 1-rotational over the cyclic group. While all I-rotational Steiner 2
-designs constructed in the past have exactly one short block-orbit, ill th
is paper we also consider I-rotational Steiner 2-designs not having this pr
operty. We call them singular and we show that they are quite rare. In part
icular, we enumerate all the abelian 1-rotational 2-(49, 4, 1) designs. (C)
1999 Academic Press.