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The Number of Prime Factors of the Scale Function on a Compactly Generated Group is Finite
Author(s) -
Willis George A.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/33.2.168
Subject(s) - mathematics , prime (order theory) , prime number , group (periodic table) , function (biology) , combinatorics , scale (ratio) , finite group , discrete mathematics , pure mathematics , physics , quantum mechanics , evolutionary biology , biology
It is shown that for each compactly generated totally disconnected locally compact group G , there is a finite number of prime numbers, p 1 , p 2 , …, p n , such that the scale function s : G → N satisfies s ( x ) = p 1 a 1 ( x )p 2 a 2 ( x )… p n a n ( x ), where x ∈ G .