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An inverse function theorem for free groups. (English) Zbl 0274.20032


MSC:

20E05 Free nonabelian groups
20E99 Structure and classification of infinite or finite groups
20E36 Automorphisms of infinite groups
57M05 Fundamental group, presentations, free differential calculus
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References:

[1] E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. · Zbl 0077.02101
[2] Daniel E. Cohen, Groups of cohomological dimension one, Lecture Notes in Mathematics, Vol. 245, Springer-Verlag, Berlin-New York, 1972. · Zbl 0231.20018
[3] Ralph H. Fox, Free differential calculus. I. Derivation in the free group ring, Ann. of Math. (2) 57 (1953), 547 – 560. · Zbl 0050.25602
[4] Nathan Jacobson, Lectures in Abstract Algebra. Vol. I. Basic Concepts, D. Van Nostrand Co., Inc., Toronto, New York, London, 1951. · Zbl 0044.26002
[5] Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. · Zbl 0138.25604
[6] M. Susan Montgomery, Left and right inverses in group algebras, Bull. Amer. Math. Soc. 75 (1969), 539 – 540. · Zbl 0174.31204
[7] B. H. Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66 (1949), 202 – 252. · Zbl 0035.30401
[8] Elvira Strasser Rapaport, On free groups and their automorphisms, Acta Math. 99 (1958), 139 – 163. · Zbl 0080.01705
[9] J. H. C. Whitehead, On certain sets of elements in a free group, Proc. London Math. Soc. 41 (1936), 48-56. · Zbl 0013.24801
[10] J. H. C. Whitehead, On equivalent sets of elements in a free group, Ann. of Math. (2) 37 (1936), no. 4, 782 – 800. · Zbl 0015.24804
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