Proposition

Lemma 64. A nontrivial fenced interval cannot be an interval in a finite soluble group. Consequently, if Inn(T)≤B≤H(T) , the interval [B,H] is not nontrivially fenced.

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ProveOct 21, 2026

Lemma 3 ([Labels]). Suppose that [D,X] is fenced, and put F_X=core_X(D) =⋂_ g∈X…Lemma 63. Let T be a finite nonabelian simple group and let Inn(T)≤H(T) . Every…Proposition

Lemma 3 ([Labels]) would give a nonabelian simple composition factor of the soluble top group. For the second assertion, quotient by Inn(T) , which is contained in the bottom B . The resulting interval lies in the soluble group Out(T) , by Schreier's Theorem.

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