Complex sentence: The group's unusual name was provided by the poet Allen Ginsberg; following one of his lectures in Boston, the group (which had just begun to play together) raised their hands and asked him to name their band.
Split into simpler sentences: The group's unusual name was provided by the poet Allen Ginsberg. Following one of his lectures in Boston, the group (which had just begun to play together) raised their hands and asked him to name their band.