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Algebraic extensions in free groups. (English) Zbl 1160.20022

Arzhantseva, Goulnara N. (ed.) et al., Geometric group theory. Geneva and Barcelona conferences. Selected papers of the conference on asymptotic and probabilistic methods in geometric group theory, Geneva, Switzerland, June 20–25, 2005 and the Barcelona conference in group theory, Barcelona, Spain, June 28 – July 3, 2005. Basel: Birkhäuser (ISBN 978-3-7643-8411-1/hbk). Trends in Mathematics, 225-253 (2007).
The paper unifies the points of view of three recent and independent papers by E. Ventura [Contemp. Math. 296, 231-255 (2002; Zbl 1025.20012)], S. Margolis, M. Sapir and P. Weil [Int. J. Algebra Comput. 11, No. 4, 405-445 (2001; Zbl 1027.20036)] and I. Kapovich and A. Miasnikov [J. Algebra 248, No. 2, 608-668 (2002; Zbl 1001.20015)], where similar modern versions of a 1951 theorem of M. Takahasi [Osaka Math. J. 3, 221-225 (1951; Zbl 0044.01106)] are given. The theory of algebraic extensions for free groups is developed and applied.
For the entire collection see [Zbl 1118.20001].

MSC:

20E22 Extensions, wreath products, and other compositions of groups
20E05 Free nonabelian groups
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