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On the structure of one-relator products of locally indicable groups with centre. (English) Zbl 0981.20023

Generalizing the result of A. Pietrowski [Math. Z. 136, 95-106 (1974; Zbl 0264.20029)] on one-relator groups with centre the author describes the structure of one-relator products of locally indicable groups with centre.

MSC:

20F05 Generators, relations, and presentations of groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
57M15 Relations of low-dimensional topology with graph theory

Citations:

Zbl 0264.20029
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Full Text: DOI

References:

[1] S.D. Brodskiı̆, Anomalous products of locally indicable groups, in: D.I. Moldavanskii (Ed.), Algebraicheskie Sistemy, Ivanovo State University Publications, Ivanovo, 1981, pp. 51-77 (in Russian).; S.D. Brodskiı̆, Anomalous products of locally indicable groups, in: D.I. Moldavanskii (Ed.), Algebraicheskie Sistemy, Ivanovo State University Publications, Ivanovo, 1981, pp. 51-77 (in Russian).
[2] Cohen, D. E., Combinatorial Group Theory: A Topological Approach, London Mathematical Society Student Texts, vol. 14 (1989), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0697.20001
[3] D.E. Cohen, Groups with free subgroups of finite index, in: Conference on Group Theory, University of Winsconsin-Parkside, 1972, Lecture Notes in Mathematics, vol. 319, Springer, Berlin, 1973, pp. 26-44.; D.E. Cohen, Groups with free subgroups of finite index, in: Conference on Group Theory, University of Winsconsin-Parkside, 1972, Lecture Notes in Mathematics, vol. 319, Springer, Berlin, 1973, pp. 26-44.
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[7] Howie, J., On pairs of 2-complexes and system of equations over groups, J. Reine Angew. Math., 324, 119-122 (1981)
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[10] Karass, A.; Solitar, D., The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc., 150, 227-255 (1970) · Zbl 0223.20031
[11] Magnus, W.; Karass, A.; Solitar, D., Combinatorial Group Theory, 2nd revised edition (1976), Dover Publications: Dover Publications New York
[12] Meskin, S.; Pietrowski, A.; Steinberg, A., One-relator groups with centre, J. Austral. Math. Soc., 16, 319-323 (1973) · Zbl 0273.20029
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