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Presentations of groupoids, with applications to groups

Published online by Cambridge University Press:  24 October 2008

P. J. Higgins
Affiliation:
King's College, London

Extract

1. Introduction. In (7), a theory was developed which dealt with certain classes of partial algebras in which the domains of the operators were determined by an ‘operator scheme’. This device allows the use of methods normally available only for full abstract algebras. In particular, one can present suitable partial algebras by means of generators and relations.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Berge, C.Théorie des graphes et ses applications (Dunod; Paris, 1958).Google Scholar
(2)Brandt, H.Über eine Verallgemeinerung des Gruppenbegriffes. Math. Ann. 96 (1927), 360366CrossRefGoogle Scholar
(3)Ehresmann, C.Gattungen von lokalen Strukturen. Jber. Deutsch. Math. Verein. 60 (1957), Abt. 1, 4977.Google Scholar
(4)Grothendieck, A.Sur quelques points d'algèbre homologique. Tôhoku Math. J. 9 (1957), 119221Google Scholar
(5)Hall, Marshall JrThe theory of groups (Macmillan; New York, 1959).Google Scholar
(6)Hasse, M.Einige Bemerkung über Graphen, Kategorien und Gruppoide. Math. Nachr. 22 (1960), 255270CrossRefGoogle Scholar
(7)Higgins, P. J.Algebras with a scheme of operators. Math. Nachr. (to appear).Google Scholar
(8)Isbell, J. R.Some remarks concerning categories and subspaces. Canad. J. Math. 9 (1957), 563577CrossRefGoogle Scholar
(9)Kuroš, A. G.The theory of groups (Chelsea; New York, 1955).Google Scholar
(10)Maclane, S.A proof of the subgroup theorem for free products. Mathematika, 5 (1958), 1319CrossRefGoogle Scholar
(11)Neumann, Hanna. Generalised free products with amalgamated subgroups.II. American J. Math. 71 (1949), 491540CrossRefGoogle Scholar
(12)Weir, A. J.The Reidemeister–Schreier and Kuroš subgroup theorems. Mathematika, 3 (1956), 4755CrossRefGoogle Scholar