Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 649.20024
Autor: Erdös, Pál; Pálfy, Péter Pál
Title: On the order of directly indecomposable groups. (In Hungarian. RU, English summary)
Source: Mat. Lapok 33, No.4, 289-298 (1986).
Review: Indecomposable groups of arbitrary even order are easily constructed. In contrast, we show that almost all odd numbers n (i.e., with the exception of a set of density 0) have (1+o(1))prod (1-(p-1)-1) log log n prime divisors such that the corresponding Sylow subgroup is a direct factor in every group of order n. The following result holds again for almost all n. Let n = n1n2 be a factorization such that all groups of order n decompose as a direct product of subgroups of order n1 and n2. Then one of the direct factors is always a cyclic group.
Reviewer: P.P.Pálfy
Classif.: * 20D60 Arithmetic and combinatorial problems on finite groups
20D40 Products of subgroups of finite groups
11N05 Distribution of primes
Keywords: Indecomposable groups; Sylow subgroup; factorization; direct product of subgroups
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