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On τ-Closed Formations of n-Ary Group


We prove that if G is a nonsingle-element n-ary finite group that belongs to a τ-closed formation \(\mathfrak{F}\), then \(G/{\text{soc(}}G{\text{)}} \in \Phi _\tau (\mathfrak{F})\), where \(\Phi _\tau (\mathfrak{F})\) is the intersection of all maximal τ-closed subformations of the τ-closed formation of n-ary groups \(\mathfrak{F}\).

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Al Dababseh Avni Faez On τ-Closed Formations of n-Ary Group. Ukrainian Mathematical Journal 53, 129–133 (2001).

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  • Finite Group