Cauty, Robert Compact Maltsev spaces that are not retracts of compact groups. (Espaces de Maltsev compacts qui ne sont pas des rétractes de groupes compacts.) (French) Zbl 0893.22002 Bull. Pol. Acad. Sci., Math. 46, No. 1, 67-70 (1998). Let \(X\) be a topological space. A Maltsev operation on \(X\) is, by definition, a mapping \(m:X^3\to X\) satisfying \(m(x,y,y) =m(y,y,x) =x\) identically. The following known results are quoted: every retract of a topological group is a Maltsev space; every compact Maltsev space is a retract of its free topological group [see P. M. Gartside, E. A. Reznichenko and D. V. Sipacheva, Topology Appl. 80, 115-129 (1997)]. The following question posed there is answered in the negative, in the paper under review: is every compact Maltsev space a retract of some compact group? Specifically, Prop. 2 states that if a finite, simply connected CW-complex has \(p\)-torsion, for some prime \(p\geq 7\), then it is not a retract of any compact group. Furthermore, it is shown that for every prime \(p\geq 7\), there exist CW-complexes which are also Maltsev spaces, satisfying the assumptions of Prop. 2. The proofs are extremely sketchy; they draw heavily upon homotopy and Lie group theory, and the theory of \(H\)-spaces. Reviewer: P.Flor (Graz) MSC: 22C05 Compact groups 54C15 Retraction Keywords:topological group; Maltsev space; free topological group; CW-complex PDFBibTeX XMLCite \textit{R. Cauty}, Bull. Pol. Acad. Sci., Math. 46, No. 1, 67--70 (1998; Zbl 0893.22002)