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The Number of Pairwise Non‐Commuting Elements and the Index of the Centre in a Finite Group
Author(s) -
Pyber L.
Publication year - 1987
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-35.2.287
Subject(s) - pairwise comparison , index (typography) , group (periodic table) , mathematics , statistics , combinatorics , computer science , physics , world wide web , quantum mechanics
If the group G contains at most n pairwise non‐commuting elements, then | G : Z ( G )| ⩽ c n for some constant c . This answers a question of B. H. Neumann and also solves a problem of P. Erdös.