Corrigendum and addendum to: “Centralizers of finite subgroups in Hall’s universal group”. (English) Zbl 1453.20050
Summary: In Hall’s universal group every non-trivial conjugacy class satisfies \(CC=U\). Hence generalized version of J. G. Thompson’s conjecture is true for every non-trivial conjugacy class \(C\) in \(U\). Moreover Ore’s conjecture (every element is a commutator) is true for \(U\) is added to [the authors, ibid. 138, 283–288 (2017; Zbl 1380.20039)]. In [loc. cit., Theorem 2.4] \(C_U(F)/Z(F)\cong U\) is true if \(Z(F)=1\).
MSC:
| 20F50 | Periodic groups; locally finite groups |
| 20E32 | Simple groups |
| 20B35 | Subgroups of symmetric groups |
| 20E07 | Subgroup theorems; subgroup growth |
Citations:
Zbl 1380.20039References:
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