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Profinite Groups with Polynomial Subgroup Growth
Author(s) -
Segal Dan,
Shalev Aner
Publication year - 1997
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/s0024610797004894
Subject(s) - profinite group , mathematics , extension (predicate logic) , normal subgroup , finitely generated abelian group , polynomial , index of a subgroup , pure mathematics , characteristic subgroup , group (periodic table) , combinatorics , computer science , mathematical analysis , physics , quantum mechanics , programming language
We characterise the profinite groups with polynomial subgroup growth. We deduce that the property PSG is extension‐closed in the category of all groups, and subgroup‐closed in the category of finitely generated profinite groups.