• Title/Summary/Keyword: normal subgroups

Search Result 180, Processing Time 0.031 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.

INTUITIONISTIC FUZZY NORMAL SUBGROUPS AND INTUITIONISTIC FUZZY COSETS

  • HUR, KUL;JANG, SU YEON;KANG, HEE WON
    • Honam Mathematical Journal
    • /
    • v.26 no.4
    • /
    • pp.559-587
    • /
    • 2004
  • We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.

  • PDF

INTUITIONISTIC FUZZY SUBGROUPS

  • AHN, TAE-CHON;HUR, KUL;JANG, KYUNG-WON;ROH, SEOK-BEOM
    • Honam Mathematical Journal
    • /
    • v.28 no.1
    • /
    • pp.31-44
    • /
    • 2006
  • We discuss various types of sublattice of the lattice of intuitionistic fuzzy subgroups of a given group. We prove that a special class of intuitionitic fuzzy normal subgroups constitutes a modular sublattice of the lattice of intuitionistic fuzzy subgroups.

  • PDF

ON INTUITIONISTIC FUZZY R-SUBGROUPS OF NEAR-RINGS

  • CHO YONG UK;JUN YOUNG BAE
    • Journal of applied mathematics & informatics
    • /
    • v.18 no.1_2
    • /
    • pp.665-677
    • /
    • 2005
  • The notion of normal intuitionistic fuzzy R-subgroups in near-rings is introduced, and related properties are investigated. Characterization of an intuitionistic fuzzy R-subgroup is given. Using a collection of right R-subgroups, an intuitionistic fuzzy right R-subgroup is established. Using a chain of right R-subgroups, an intuitionistic fuzzy right R-subgroup is also established.