ENUMERATING FINITE GROUPS
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This paper deals with the problem of enumerating the number f(n) of isomorphism types of groups of order n. There are three results which give upper bounds for f(n). The first bound holds for arbitrary groups, the second one deals with solvable groups, while the third one applies to groups with abelian Sylow subgroups. In this article similar methods are used as in a predecessor [ibid. 20, 395-401 (1969; Zbl 0204.347)] (for instance bounds for the order of certain degree 2 cohomology groups). The note also contains a detailed discussion of related results.
- University of Oxford United Kingdom
- Queen's University Canada
isomorphism types of groups, upper bounds, Arithmetic functions; related numbers; inversion formulas, number of groups, Asymptotic results on arithmetic functions, Asymptotic results on counting functions for algebraic and topological structures, Arithmetic and combinatorial problems involving abstract finite groups, solvable groups
isomorphism types of groups, upper bounds, Arithmetic functions; related numbers; inversion formulas, number of groups, Asymptotic results on arithmetic functions, Asymptotic results on counting functions for algebraic and topological structures, Arithmetic and combinatorial problems involving abstract finite groups, solvable groups
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