Geodesic
The Free Product of Two Groups with a Malnormal Amalgamated Subgroup
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 933-959

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

In [1], B. Baumslag defined a subgroup U of a group G to be malnormal in G if gug –1 ∈ U, 1 ≠ u ∈ U, implies that g ∈ U. Baumslag considered the class of amalgamated products (A * B; U) in which U is malnormal in both A and B. These amalgamated products play an important role in the investigations of B. B. Newman [13] of groups with one defining relation having torsion. In this paper, we shall be concerned primarily with a generalization of this class.Let U be a subgroup of a group G and let u ∈ U. Then the extended normalizer EG(u, U) of u relative to U in G is defined by if u ≠ 1, and by EG(u, U) = U if u = 1. 
Karrass, A.; Solitar, D. The Free Product of Two Groups with a Malnormal Amalgamated Subgroup. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 933-959. doi: 10.4153/CJM-1971-102-8
@article{10_4153_CJM_1971_102_8,
     author = {Karrass, A. and Solitar, D.},
     title = {The {Free} {Product} of {Two} {Groups} with a {Malnormal} {Amalgamated} {Subgroup}},
     journal = {Canadian journal of mathematics},
     pages = {933--959},
     year = {1971},
     volume = {23},
     number = {5},
     doi = {10.4153/CJM-1971-102-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-102-8/}
}
TY  - JOUR
AU  - Karrass, A.
AU  - Solitar, D.
TI  - The Free Product of Two Groups with a Malnormal Amalgamated Subgroup
JO  - Canadian journal of mathematics
PY  - 1971
SP  - 933
EP  - 959
VL  - 23
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-102-8/
DO  - 10.4153/CJM-1971-102-8
ID  - 10_4153_CJM_1971_102_8
ER  - 
%0 Journal Article
%A Karrass, A.
%A Solitar, D.
%T The Free Product of Two Groups with a Malnormal Amalgamated Subgroup
%J Canadian journal of mathematics
%D 1971
%P 933-959
%V 23
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-102-8/
%R 10.4153/CJM-1971-102-8
%F 10_4153_CJM_1971_102_8

[1] 1. Baumslag, B., Generalized free products whose two-generator subgroups are free, J. London Math. Soc. 43 (1968), 601–606. Google Scholar

[2] 2. Baumslag, G., On generalized free products, Math. Z. 75 (1962), 423–438. Google Scholar

[3] 3. Greenberg, L., Discrete groups of motions, Can. J. Math. 12 (1960), 414–425. Google Scholar

[4] 4. Higman, G., Neumann, B. H., and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247–254. Google Scholar

[5] 5. Karrass, A., Magnus, W., and Solitar, D., Elements of finite order in groups with a single defining relation, Comm. Pure Appl. Math. 18 (1960), 57–66. Google Scholar

[6] 6. Karrass, A. and Solitar, D., The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227–255. Google Scholar

[7] 7. Karrass, A. and Solitar, D., Subgroups of HNN groups and groups with one defining relation, Can. J. Math. 28 (1971), 627–643. Google Scholar

[8] 8. Lewin, T., Finitely generated D-groups, J. Austral. Math. Soc. 7 (1967), 375–409. Google Scholar

[9] 9. Magnus, W., Karrass, A., and Solitar, D., Combinatorial group theory: Presentations of groups, Pure and Appl. Math., Vol. 13 (Interscience, New York, 1966). Google Scholar

[10] 10. Moldavanski, D. I., Certain subgroups of groups with one defining relation, Sibirsk. Mat. Z. 8 (1967), 1370–1384. Google Scholar

[11] 11. Neumann, B. H., An essay on free products with amalgamations, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 503–544. Google Scholar

[12] 12. Neumann, H., Generalized free products with amalgamated subgroups. II, Amer. J. Math. 71 (1949), 491–540. Google Scholar

[13] 13. Newman, B. B., Some aspects of one-relator groups, Ph.D. thesis, University of Canberra, 1969 (submitted to Acta Math.). Google Scholar

[14] 14. Scott, W. R., Group theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1964). Google Scholar

Cité par Sources :