Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 16
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Glauberman, George and Lynd, Justin 2016. Control of fixed points and existence and uniqueness of centric linking systems. Inventiones mathematicae,

    Rowley, Peter and Taylor, Paul 2016. An algorithm for the Thompson subgroup of a p-group. Journal of Algebra, Vol. 461, p. 375.

    Cantarero, José Scherer, Jérôme and Viruel, Antonio 2014. Nilpotent $p\mspace{1mu}$ -local finite groups. Arkiv för Matematik, Vol. 52, Issue. 2, p. 203.

    Green, David J. and Lynd, Justin 2013. Weak closure and Oliver’s p-group conjecture. Israel Journal of Mathematics, Vol. 197, Issue. 1, p. 497.

    Lynd, Justin 2013. 2-subnormal quadratic offenders and Oliver's p-group conjecture. Proceedings of the Edinburgh Mathematical Society, Vol. 56, Issue. 01, p. 211.

    Oliver, Bob 2013. Existence and uniqueness of linking systems: Chermak’s proof via obstruction theory. Acta Mathematica, Vol. 211, Issue. 1, p. 141.

    Seeliger, Nora 2012. Group models for fusion systems. Topology and its Applications, Vol. 159, Issue. 12, p. 2845.

    Green, David J. Héthelyi, László and Mazza, Nadia 2011. On a strong form of Oliverʼs p-group conjecture. Journal of Algebra, Vol. 342, Issue. 1, p. 1.

    Green, David J. Héthelyi, László and Mazza, Nadia 2010. On Oliver’s p-group conjecture: II. Mathematische Annalen, Vol. 347, Issue. 1, p. 111.

    Castellana, Natàlia and Libman, Assaf 2009. Wreath products and representations of p-local finite groups. Advances in Mathematics, Vol. 221, Issue. 4, p. 1302.

    Libman, Assaf and Viruel, Antonio 2009. On the homotopy type of the non-completed classifying space of a p-local finite group. Forum Mathematicum, Vol. 21, Issue. 4,

    Onofrei, Silvia and Stancu, Radu 2009. A characteristic subgroup for fusion systems. Journal of Algebra, Vol. 322, Issue. 5, p. 1705.

    Green, David Héthelyi, László and Lilienthal, Markus 2008. On Oliver’sp-group conjecture. Algebra & Number Theory, Vol. 2, Issue. 8, p. 969.

    Oliver, Bob and Ventura, Joana 2007. Extensions of linking systems with p-group kernel. Mathematische Annalen, Vol. 338, Issue. 4, p. 983.

    Ragnarsson, Kári 2006. Classifying spectra of saturated fusion systems. Algebraic & Geometric Topology, Vol. 6, Issue. 1, p. 195.

    Ragnarsson, Kári 2006. Alternative stable homotopy classification of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals=""><mml:msubsup><mml:mrow><mml:mi mathvariant="italic">BG</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>∧</mml:mo></mml:mrow></mml:msubsup></mml:math>. Topology, Vol. 45, Issue. 3, p. 601.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 137, Issue 2
  • September 2004, pp. 321-347

Equivalences of classifying spaces completed at odd primes

  • BOB OLIVER (a1)
  • DOI:
  • Published online: 01 September 2004

We prove the Martino–Priddy conjecture for an odd prime $p$: the $p$-completions of the classifying spaces of two groups $G$ and $G^\prime$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $p$-subgroups which preserves fusion. A second theorem is a description for odd $p$ of the group of homotopy classes of self homotopy equivalences of the $p$-completion of $BG$, in terms of automorphisms of a Sylow $p$-subgroup of $G$ which preserve fusion in $G$. These are both consequences of a technical algebraic result, which says that for an odd prime $p$ and a finite group $G$, all higher derived functors of the inverse limit vanish for a certain functor $\calz_G$ on the $p$-subgroup orbit category of $G$.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *