Camina, Rachel The Nottingham group. (English) Zbl 0977.20020 du Sautoy, Marcus (ed.) et al., New horizons in pro-\(p\) groups. Boston, MA: Birkhäuser. Prog. Math. 184, 205-221 (2000). The paper under review provides an extremely useful survey of the current knowledge about the so-called Nottingham group \(\mathcal N\), and of the techniques that have been used to investigate it. This group has been studied originally by group-theorists as a group of power series under substitution; see the papers by S. A. Jennings [Can. J. Math. 6, 325-340 (1954; Zbl 0058.02201)], D. L. Johnson [J. Aust. Math. Soc., Ser. A 45, No. 3, 296-302 (1988; Zbl 0666.20016)] and his Ph.D.student I. O. York [Proc. Edinb. Math. Soc., II. Ser. 33, No. 3, 483-490 (1990; Zbl 0723.20010)]. \(\mathcal N\) can be also regarded, number-theoretically, as the group of wild automorphisms of the local field \(\mathbb{F}_q( (t))\); this approach has led among others to the striking result by the author, that every countably-based pro-\(p\) group can be embedded in \(\mathcal N\) [J. Algebra 196, No. 1, 101-113 (1997; Zbl 0883.20015)].As the author notes, the Nottingham group on the one hand lends itself to detailed and computational investigations; on the other hand, it exhibits many interesting properties, thus providing many examples and counterexamples. This paper is a very handy reference for such an interesting object.For the entire collection see [Zbl 0945.00009]. Reviewer: A.Caranti (Povo) Cited in 7 ReviewsCited in 45 Documents MSC: 20E18 Limits, profinite groups 20-02 Research exposition (monographs, survey articles) pertaining to group theory Keywords:\(p\)-groups; pro-\(p\)-groups; Nottingham group; groups of power series Citations:Zbl 0058.02201; Zbl 0666.20016; Zbl 0723.20010; Zbl 0883.20015 × Cite Format Result Cite Review PDF