with R. Biggers, Moduli spaces of covers and the Hurwitz monodromy group: Crelle's Journal 335 (1982), 87–121. This pdf file has been scanned, but is searchable. By the late 70s there was motivation to find serious examples of Hurwitz spaces defined by a Nielsen class where there were several components. This paper has the first: an unbraidable outer automorphism. Such examples – and the components identified by Schur multipliers – remain the most interesting, non-accidental identifiers of components. For example Alternating groups and moduli space lifting Invariants. The subject has advanced greatly from this time.

• This paper contains a list of lemmas used often in other papers, such as that inner automorphims are always braidable.
• Non-braidable outer automorphisms preserving a Nielsen class are a big topic since they happen in such applications as generalizing Serre's Open Image Theorem all the time.
• The main problem of the paper, is deciding the existence of total representing families for Hurwitz spaces in the étale topology, a topic of § 4 of Fields of Definition of Function Fields and Hurwitz Families Groups as Galois Groups
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