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Injectors in Certain Profinite and Locally Finite Groups
Author(s) -
Tomkinson M. J.
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/s002461079700481x
Subject(s) - locally nilpotent , mathematics , countable set , nilpotent , nilpotent group , pure mathematics , profinite group , class (philosophy) , injector , series (stratigraphy) , group (periodic table) , locally finite group , discrete mathematics , physics , computer science , paleontology , quantum mechanics , artificial intelligence , biology , thermodynamics , abelian group
Fitting classes and their associated injectors have been considered in a number of classes of locally finite groups [ 9 , 8 , 4 , 5 ]. In particular, Dixon has considered the class L of countable locally finite groups with min − p for all primes p . He has shown that if the L‐group G is radical (that is, it has an ascending locally nilpotent series) then G has locally nilpotent injectors, any two of which are isomorphic. Question 7.4.7 in [ 5 ] asks whether the restriction of being radical can be removed in this result.