• Title/Summary/Keyword: locally nilpotent groups

Search Result 2, Processing Time 0.046 seconds

LOCALLY NILPOTENT GROUPS WITH THE MAXIMAL CONDITION ON INFINITE NORMAL SUBGROUPS

  • Paek, Dae-Hyun
    • Bulletin of the Korean Mathematical Society
    • /
    • v.41 no.3
    • /
    • pp.465-472
    • /
    • 2004
  • A group G is said to satisfy the maximal condition on infinite normal subgroups if there does not exist an infinite properly ascending chain of infinite normal subgroups. We characterize the structure of locally nilpotent groups satisfying this chain condition. We then show how to construct locally nilpotent groups with the maximal condition on infinite normal subgroups, but not the maximal condition on subgroups.

LOCALLY NILPOTENT GROUPS WITH THE MINIMAL CONDITION ON NORMAL SUBGROUPS OF INFINITE INDEX

  • Paek, Dae-Hyun
    • Bulletin of the Korean Mathematical Society
    • /
    • v.41 no.4
    • /
    • pp.779-783
    • /
    • 2004
  • A group G is said to satisfy the minimal condition on normal subgroups of infinite index if there does not exist an infinite properly descending chain $G_1$ > $G_2$ > ... of normal subgroups of infinite index in G. We characterize the structure of locally nilpotent groups satisfying this chain condition.