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Hypercentral Groups with all Subgroups Subnormal III
Author(s) -
Smith Howard
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/s0024609301008293
Subject(s) - mathematics , nilpotent , bounded function , group (periodic table) , nilpotent group , combinatorics , pure mathematics , chemistry , mathematical analysis , organic chemistry
It is shown that a hypercentral group that has all subgroups subnormal and every non‐nilpotent subgroup of bounded defect is nilpotent. As a consequence, a hypercentral group of length at most ω in which every subgroup is subnormal is nilpotent. 2000 Mathematics Subject Classification 20E15, 20F14.