References
S. I.Adian, On the word problem for groups defined by periodic relations. In: Burnside Groups, J. L. Mennicke, ed., LNM806, 41–46. Berlin-Heidelberg-New York 1980.
M. Culler, Using surfaces to solve equations in free groups. Topology20, 133–145 (1981).
A. Dold, Nullhomologous words in free groups which are not nullhomologous in any proper subgroup. Arch. Math.50, 564–569 (1988).
V. G. Durnev, The Mal'tsev-Nielsen equation in a free metabelian group of rank two. Math. Notes64, 927–929 (1989).
C. C. Edmunds, On the endomorphism problem for free groups II. Proc. London Math. Soc. (3)38, 153–168 (1979).
M. R.Garey and D. S.Johnson, Computers and intractability, a guide to the theory ofNP-completeness. New York 1979.
N. Gupta andV. Shpilrain, Nielsen's commutator test for two-generator groups. Math. Proc. Cambridge Philos. Soc.114, 295–301 (1993).
P. Hill andS. J. Pride, Commutators, generators, and conjugacy equations in groups, Arch. Math.44, 1–14 (1985).
S. V. Ivanov, The free Burnside groups of sufficiently large exponents. Internat. J. Algebra Comp.4, 1–308 (1994).
R. N. Kalia andG. Rosenberger, Automorphisms of the Fuchsian groups of type (0,2,2,2,q:0). Comm. Algebra6, 115–129 (1978).
Y. G. Kleiman, On identities in groups (Russian). Trudy Moskov. Mat. Obshch.44, 62–108 (1982).
R. C. Lyndon, The equationa 2 b 2=c 2 in free groups. Michigan Math. J.6, 89–95 (1959).
R. C.Lyndon and P. E.Schupp, Combinatorial group theory. Berlin-Heidelberg-New York 1977.
G. S. Makanin, Equations in a free group. Math. USSR-Izv.21, 483–546 (1983).
M.Hall, Jr., The theory of groups. New York 1959.
H.Neumann, Varieties of groups. Berlin-Heidelberg-New York 1967.
J. Nielsen, Die Automorphismen der allgemeinen unendlichen Gruppe mit zwei Erzeugenden. Math. Ann.78, 385–397 (1918).
E. Rips, Commutator equations in free groups. Israel J. Math.39, 326–340 (1981).
G. Rosenberger, Eine Bemerkung zu den triangl-Gruppen. Math. Z.132, 239–244 (1973).
G. Rosenberger, Alternierende Produkte in freien Gruppen. Pacific J. Math.78, 243–250 (1978).
G.Rosenberger, Minimal generating systems for plane discontinuous groups and an equation in free groups. In: Proceedings of Groups-Korea 1988, 170–186. Berlin-Heidelberg-New York 1989.
G. Rosenberger, A property of subgroups of free groups. Bull. Austral. Math. Soc.43, 269–272 (1991).
V.Shpilrain, Test elements for endomorphisms of free groups and algebras. Preprint.
V. Shpilrain, Recognizing automorphisms for the free groups. Arch. Math.62, 385–392 (1994).
J. R.Stallings, Problems about free quotients of groups. Preprint.
E. C.Turner, Test words for automorphisms of free groups. Bull. London Math. Soc., to appear.
M. J. Wicks, Commutators in free products. J. London Math. Soc. (2)37, 433–444 (1962).
M. J.Wicks, The equationx 2 y 2=g over free products. In: Proceedings of the Second Congress of the Singapore National Academy of Science 1973, 238–248.
H. Zieschang, Alternierende Produkte in freien Gruppen. Abh. Math. Sem. Univ. Hamburg27, 12–31 (1964).
H. Zieschang, Über Automorphismen ebener discontinuierlicher Gruppen. Math. Ann.166, 148–167 (1966).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Comerford, L.P. Generic elements of free groups. Arch. Math 65, 185–195 (1995). https://doi.org/10.1007/BF01195088
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01195088