In a paper from 1980, Shelah constructed a Jonsson group of

size Aleph_1.

Assuming CH, he moreover obtained what is now known as a

"Shelah group" of size Aleph_1, i.e., a group of size Aleph_1 such that

for some integer N, the collection of all N-sized words over the

alphabet of any given uncountable subset of the group resurrects the

whole group.

In this talk, we shall present a ZFC construction of a Shelah group at

the level of any successor of a regular cardinal. We shall also address

the problem of constructing Shelah groups at successors of singulars and

at inaccessibles.