Recognising dualities in finite simple groups

M. Costantini; S. E. Stonehewer; G. Zacher

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Recognising dualities in finite simple groups

机译：在有限的简单组中识别二元性

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Given a group G, subgroup K of G is called cocyclic (in G) if the interval [G/K] is anti-isomorphic to the lattice of subgroups of a cyclic group. Let us denote by CG the partially ordered set of all cyclic subgroups of G and by Co G the partially ordered set of all cocyclic subgroups of G. We shall consider groups G, G-bar for which the following properties hold: D_1: there exists an anti-isomorphism τ of Co G onto C(G-bar), D_2: every subgroup of G is the intersection of cocyclic subgroups, D_3: if X, Y, Z are cocyclic subgroups of G, then X ≥ Y ∩ Z if and only if X~τ ≤ .

机译：如果间隔[g / k]是循环组的亚组晶粒的抗体，则给出G组G的亚组K被称为共循环（以g）。让我们通过CG表示G的部分有序集G和CO G的全循环子组的全部循环子组。我们将考虑以下属性的G，G-BAR组，其中包括以下属性：D_1：存在 CO g上的抗构素τ（g-bar），d_2：g的每个亚组是Cocyclic子组，D_3：如果x，y，z是g，那么x≥y∩zi 只有x〜τ≤。

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《Journal of group theory》 |2001年第4期|共19页
作者
M. Costantini; S. E. Stonehewer; G. Zacher;
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Dipartimento di matematica pura ed applicata Universita di Padova Via Belzoni 7 35131 Padova Italy;

Mathematics Institute University of Warwick Coventry CV4 7AL England;

Dipartimento di matematica pura ed applicata Universita di Padova Via Belzoni 7 35131 Padova Italy;

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Recognising dualities in finite simple groups

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