فهرست مطالب

International Journal of Group Theory
Volume:14 Issue: 1, Mar 2025

  • تاریخ انتشار: 1403/07/08
  • تعداد عناوین: 4
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  • DOUBLE CHAIN CONDITION ON NON-ASCENDANT SUBGROUPS
    Jia Zhang * Pages 1-7

    If $\theta$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $\theta$-subgroups if it admits no infinite double chain $$\cdots<X_{-n}<\cdots<X_{-1}<X_0<X_1<\cdots<X_n<\cdots$$ consisting of $\theta$-subgroups. Here we want to describe the structure of locally finite and locally nilpotent groups satisfying the double chain condition on non-ascendant subgroups in term of chain conditions and of ascendant subgroups.

    Keywords: Double Chains, Ascendant Subgroups, Locally Finite Groups, Locally Nilpotent Groups
    Abstract View Paper Research/Original Article Original: English
  • Groups with the real chain condition on non-pronormal subgroups
    Ulderico Dardano *, Fausto De Mari Pages 9-18
    It is shown that a generalised radical group has no chain of non-pronormal subgroups with the same order type as the set $\mathbb{R}$ of the real numbers if and only if either the group is minimax or all subgroups are pronormal.
    Keywords: Pronormal Subgroup, Minimax Group, Weak Chain Condition, Deviation
    Abstract View Paper Research/Original Article Original: English
  • On groups with many normal subgroups
    Alessio Russo *, Mario Viscusi Pages 19-23
    The structure of groups which are rich in normal subgroups has been investigated by several authors. Here, we prove that if a radical group G has normal deviation, which means that the set of its non-normal subgroups satisfies a very weak chain condition, then either G is a minimax group or all its subgroups are normal.
    Keywords: Normal Subgroup, Normal Deviation, Minimax Group
    Abstract View Paper Research/Original Article Original: English
  • Generalized nilpotent braces and nilpotent groups
    Martyn Dixon *, Leonid Kurdachenko, Igor Subbotin Pages 25-45
    The authors give a brief survey of some results concerning nilpotent braces and their generalizations. Various results concerning $\star$-hypercentral and locally $\star$-nilpotent braces are given.
    Keywords: Brace, Nilpotent Brace, $, Star$-Hypercentral Brace, Locally $, Star$-Nilpotent Brace
    Abstract View Paper Research/Original Article Original: English