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Homotopy properties of the poset of nontrivial p-subgroups of a group. (English) Zbl 0388.55007


MSC:

55P10 Homotopy equivalences in algebraic topology
20F16 Solvable groups, supersolvable groups
20E07 Subgroup theorems; subgroup growth
55P15 Classification of homotopy type
55U99 Applied homological algebra and category theory in algebraic topology
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References:

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[2] Brown, K., Euler characteristics of groups: The \(p\)-fractional part, Invent. Math., 29, 1-5 (1975) · Zbl 0294.20048
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[9] Quillen, D., Higher algebraic \(K\)-theory I, (Lecture Notes in Mathematics, Vol. 341 (1973), Springer-Verlag: Springer-Verlag Berlin), 85-147 · Zbl 0292.18004
[10] Reisner, G. A., Cohen-Macaulay quotients of polynomial rings, Advances in Math., 21, 30-49 (1976) · Zbl 0345.13017
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[12] Stanley, R. P., Cohen-Macaulay complexes, (Proceedings of the Advanced Study Institute in Combinatorics. Proceedings of the Advanced Study Institute in Combinatorics, Berlin (1976)) · Zbl 0376.55007
[13] Tits, J., On buildings and their applications, (Proc. Int. Cong. of Mathematicians. Proc. Int. Cong. of Mathematicians, Vancouver (1974)) · Zbl 0336.57009
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