caa a22 4500 386385351 CHVBK 20180307112056.0 cr unu---uuuuu 161130e198903 xx s 000 0 eng 10.1017/S0305004100067700 doi S0305004100067700 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100067700 Truss J. K. Department of Pure Mathematics, University of Leeds The group of almost automorphisms of the countable universal graph [Elektronische Daten] [J. K. Truss] The group Aut Γ of automorphisms of Rado's universal graph Γ (otherwise known as the ‘random' graph: see [1]) and the corresponding groups Aut Γc for C a set of ‘colours' with 2 ≤ |C| ≤ 0, were studied in [4]. It was shown that Aut Γc is a simple group, and the possible cycle types of its members were classified. A natural extension of Aut Γc to a highly transitive permutation group on the same set is obtained by considering the ‘almost automorphisms' of Γ. It is the purpose of the present paper to answer similar questions about the resulting group AAut Γc. Namely we shall classify its normal subgroups and the cycle types of its members. The main result on normal subgroups is summed up in Corollary 2·9, which says that the non-trivial normal subgroups of AAut Γc form a lattice isomorphic to the lattice of subgroups of the free Abelian group of rank n where n = |C| - 1, and for cycle types it will be shown that those occurring in AAut Γc are precisely the same as in Aut Γc except for those which are the product of finitely many cycles. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/2(1989-03), 223-236 0305-0041 105:2<223 1989 105 PSP https://doi.org/10.1017/S0305004100067700 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100067700 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Truss J. K. Department of Pure Mathematics, University of Leeds NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/2(1989-03), 223-236 0305-0041 105:2<223 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge