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Locally Finite Groups All of Whose Subgroups are Boundedly Finite over Their Cores
Author(s) -
Cutolo G.,
Khukhro E. I.,
Lennox J. C.,
Rinauro S.,
Smith H.,
Wiegold James
Publication year - 1997
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/s0024609397003068
Subject(s) - mathematics , pure mathematics
For n a positive integer, a group G is called core‐n if H / H G has order at most n for every subgroup H of G (where H G is the normal core of H , the largest normal subgroup of G contained in H ). It is proved that a locally finite core‐ n group G has an abelian subgroup whose index in G is bounded in terms of n . 1991 Mathematics Subject Classification 20D15, 20D60, 20F30.