Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 335.20011
Autor: Erdös, Paul; Straus, E.G.
Title: How abelian is a finite group?. (In English)
Source: Linear multilinear Algebra 3, 307-312 (1976).
Review: It is shown that a finite group of order n contains an Abelian p-group whose order exceeds (1- \epsilon) log n for any \epsilon > 0 and all sufficiently large n. Let Ak(n) be the minimal number of k-tuples of elements which are pairwise commuting in a group of order n. Some estimates are given for the growth rate of Ak(n) with n. In particular it is shown that Ak+1(n)/Ak(n) ––> oo as n ––> oo for any fixed k. These estimates are closely connected with estimates for the minimal number of conjugacy classes in a group of order n. – Some related problems are discussed.
Classif.: * 20D99 Abstract finite groups
20D20 Sylow subgroups of finite groups
20K99 Abelian groups
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