Geodesic
Minimal Cockcroft subgroups
Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 87-90

Voir la notice de l'article provenant de la source Cambridge University Press

Consider any group G. A [G, 2]-complex is a connected 2-dimensional CW-complex with fundamental group G. If X is a [G, 2]-complex and L is a subgroup of G, let XL denote the covering complex of X corresponding to the subgroup L. We say that a [G, 2]-complex is L-Cockcroft if the Hurewicz map hL:π2(X)→;H2(XL) is trivial. In case L = G we call X Cockcroft. There are interesting classes of 2-complexes that have the Cockcroft property. A [G, 2]-complex X is aspherical if π2(X) = 0. It was observed in [4] that a subcomplex of an aspherical 2-complex is Cockcroft. The Cockcroft property is of interest to group theorists as well. Let X be a [G, 2]-complex modelled on a presentation (〈S; R〉 of the group G. If it can be shown that X is Cockcroft, then it follows from Hopf's theorem (see [2, p. 31]) that H2(G) is isomorphic to H2(X). In particular H2(G) is free abelian. For a survey on the Cockcroft property see Dyer [5]. A collection {Gα: α ∈ Ώ} of subgroups of a group G that is totally ordered by inclusion is called a chain of subgroups of G. Denning β ≤ α if and only if Gα ≤ Gβ makes Ώ into a totally ordered set. The main result of this paper is the following theorem. 
Harlander, Jens. Minimal Cockcroft subgroups. Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 87-90. doi: 10.1017/S0017089500030585
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[1] 1.Adams, J. F., A new proof of a theorem of W. H. Cockcroft, J. London Math. Soc. 30 (1955), 482–488. Google Scholar | DOI

[2] 2.Brown, K. S., Cohomology of groups (Springer, 1982). Google Scholar

[3] 3.Bogley, W. A., Unions of Cockcroft two-complexes, preprint. Google Scholar

[4] 4.Cockcroft, W. H., On two-dimensional aspherical complexes, Proc. London Math. Soc. (3) 4 (1954), 375–384. Google Scholar | DOI

[5] 5.Dyer, M. N., Cockcroft 2-complexes, preprint. Google Scholar

[6] 6.Howie, J., Aspherical and acyclic 2-complexes, J. London Math. Soc. (2) 20 (1979), 549–558. Google Scholar

[7] 7.Howie, J., On the fundamental group of an almost-acyclic 2-complex, Proc. Edinburgh Math. Soc. (2) 24 (1981), 119–122. Google Scholar

[8] 8.Howie, J., How to generalize one-relator group theory, Combinatorial group theory and topology, ed. Gersten, S. M. and Stallings, J. R. (Ann. of Math. Stud. 111, Princeton Univ. Press, 1987), 53–78. Google Scholar

[9] 9.Whitehead, J. H. C., On adding relations to homotopy groups, Ann. of Math. (2) 42 (1941), 409–428. Google Scholar | DOI

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