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GROUPS SATISFYING THE DOUBLE CHAIN CONDITION ON ABELIAN SUBGROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 99 / Issue 2 / April 2019
- Published online by Cambridge University Press:
- 12 September 2018, pp. 212-218
- Print publication:
- April 2019
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- Article
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- You have access
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If
$\unicode[STIX]{x1D703}$ is a subgroup property, a group 
$G$ is said to satisfy the double chain condition on 
$\unicode[STIX]{x1D703}$-subgroups if it admits no infinite double sequences consisting of
$$\begin{eqnarray}\cdots <X_{-n}<\cdots <X_{-1}<X_{0}<X_{1}<\cdots <X_{n}<\cdots\end{eqnarray}$$
$\unicode[STIX]{x1D703}$-subgroups. We describe the structure of generalised radical groups satisfying the double chain condition on abelian subgroups.
