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# Article

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Keywords:
subnormal subgroups; locally soluble-by-finite groups
Summary:
A group \$G\$ has subnormal deviation at most \$1\$ if, for every descending chain \$H_{0}>H_{1}>\dots \$ of non-subnormal subgroups of \$G\$, for all but finitely many \$i\$ there is no infinite descending chain of non-subnormal subgroups of \$G\$ that contain \$H_{i+1}\$ and are contained in \$H_{i}\$. This property \$\frak P\$, say, was investigated in a previous paper by the authors, where soluble groups with \$\frak P\$ and locally nilpotent groups with \$\frak P\$ were effectively classified. The present article affirms a conjecture from that article by showing that locally soluble-by-finite groups with \$\frak P\$ are soluble-by-finite and are therefore classified.
References:
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