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More Fraïssé Limits of Nilpotent Groups of Finite Exponent
Author(s) -
Baudisch Andreas
Publication year - 2004
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/s002460930400339x
Subject(s) - mathematics , nilpotent , nilpotent group , exponent , class (philosophy) , limit (mathematics) , prime (order theory) , categorical variable , pure mathematics , central series , mathematics subject classification , discrete mathematics , combinatorics , algebra over a field , mathematical analysis , linguistics , statistics , philosophy , artificial intelligence , computer science
The class of nilpotent groups of class c and prime exponent p > c with additional predicates P c ⊆ P c −1 ⊆ … ⊆ P 1 for suitable subgroups has the amalgamation property. Hence the Fraïssé limit D of the finite groups of this class exists. 〈1〉 ⊆ P c ( D ) ⊆ … ⊆ P 2 ( D ) ⊆ P 1 ( D ) = D is the lower and the upper central series of D . In this extended language, D is ultrahomogeneous. The elementary theory of D allows the elimination of quantifiers and it is ℵ 0 ‐categorical. For c = 2 this was proved by Baudisch in Bull. London Math. Soc. 33 (2001) 513–519. 2000 Mathematics Subject Classification 03C60, 03C98.