The lower central series in some groups with the subnormal join property

Smith, Howard

doi:10.1090/S0002-9939-1985-0792265-3

The lower central series in some groups with the subnormal join property
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Proc. Amer. Math. Soc. 94 (1985), 585-588 Request permission

Abstract:

The following question is considered: What groups $G$ are such that, given any subnormal subgroups $H$ and $K$ of $G$, with join $J$, and given any positive integers $a$ and $b$, there exists an integer $c$ such that ${\gamma _c}(J)$ is contained in ${\gamma _a}(H){\gamma _b}(K)$? It is shown that many, but not all, groups known to have the "subnormal join property" satisfy this further condition.

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Finiteness conditions and generalised soluble groups

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