On Groups in Which Every Element Has Finite Order

REFERENCES

• S. I. Adian (1974) Periodic groups of odd exponent, Lecture Notes in Math, 372, Springer-Verlag, 8–12.
   Google Scholar
• S. I. Adian, (1975), The Burnside problem and identities in groups, Grenzgeb Math. 95, Springer-Verlag 1979.
   Google Scholar
• S. I. Adian, (1984), Investigation of the Burnside problem and related questions, AN. SSR, 168, (Trudy Mat. Inst.) 171–196. [Russian]
   Google Scholar
• S. I. Adian and N. N. Repin (1986), Exponentiality of the lower bound for the nilpotency class of Engel Lie algebras, Mat. Zametki, 39, 444–452. [Russian]
   Google Scholar
• S. V. Aleshin (1972), Finite automata and the Burnside problem for periodic groups, Mat. Zametki, 11, 319–328. [Engl. Transl. Math. Notes, 11, 199–203]
   Google Scholar
• William A. Alford, George Havas, and M. F. Newman (1975), Groups of exponent four, Notices Amer. Math. Soc., 22, A.301.
   Google Scholar
• S. E. Arshon (1937), Proof of the existence of n-valued infinite asymmetric sequences, Mat. Sbornik, 2(44), 769–779. [Russian]
   Google Scholar
• S. Bachmuth, H. Y. Mochizuki, and K. Weston (1973), A group of exponent 4 with derived length at least 4, Proc. Amer. Math. Soc., 39, 228–234.
   Web of Science ®Google Scholar
• A. J. Bayes, J. Kautsky, and J. W. Wamsley (1974), Computations in nilpotent groups (applications), Proc. Second Internat. Conf. Theory of Groups, Canberra, Lecture Notes in Math. 372 (Springer-Verlag) 82–89.
   Google Scholar
• J. L. Britton (1973), The existence of infinite Burnside groups, Word Problems, North Holland, pp. 67–348.
   Google Scholar
• J. L. Britton, (1980), Erratum: The existence of infinite Burnside groups, Word Problems II, The Oxford Book, North Holland, p. 71.
   Google Scholar
• R. H. Bruck (1963), Engel conditions in groups and related questions, Lecture Notes (Canberra).
   Google Scholar
• W. Burnside (1902), On an unsettled question in the theory of discontinuous groups, Quart. J. Pure Appl. Math., 33, 230–238.
   Google Scholar
• W. Burnside (1905), On criteria of finiteness of the order of a group of linear substitutions, Proc. London Math. Soc., (2) 3, 230–238.
   Google Scholar
• Richard A. Dean (1965), A sequence without repeats in x, x^-1 y, y^-, Amer. Math. Monthly 72, 383–385.
   Web of Science ®Google Scholar
• E. S. Golod (1964), On nil-algebras and finitely approximate p-groups, Izv. Akad. Nauk. USSR Ser. Mat., 28, 273–276. [Russian]
   Google Scholar
• R. I. Grigorchuk (1980), On the Burnside problem for periodic groups, Funkcional Anal, i Prilozen, 14, 53–54 [Russian]. Engl, transl. Functional Anal. Appl., 14, 41–43.
   Google Scholar
• R. I. Grigorchuk, (1983), On Milnor's problem of group growth, Soviet Math. Dokl., 28, 23–26.
   Google Scholar
• Otto Grün (1940), Zusammenhang zwischen Potenzbildung und Kommutatorbildung, J. reine angew. Math., 182, 158–177.
   Google Scholar
• Fritz J. Grunewald, George Havas, J. L. Mennicke and M. F. Newman (1980), Groups of exponent eight, Proc. Workshop on Burnside Groups, Bielefeld (1977), Springer Lecture Notes, 806, 49–188.
   Google Scholar
• V. S. Guba (1986), A finitely generated divisible group, Izvestija Akad. Nauk SSSR Ser. Mat., 50, 883–924.
   Google Scholar
• C. K. Gupta and N. D. Gupta (1972), On groups of exponent four II, Proc. Amer. Math. Soc., 31, 360–362.
   Web of Science ®Google Scholar
• N. D. Gupta and M. F. Newman (1974), The nilpotency class of finitely generated groups of exponent four, Proc. Second Internat. Conf. Theory of Groups, Canberra, Springer Lecture Notes 372, 330–332.
   Google Scholar
• N. D. Gupta and R. B. Quintana, Jr. (1972), On groups of exponent four III, Proc. Amer. Math. Soc., 33, 15–19.
   Web of Science ®Google Scholar
• Narain Gupta and Said Sidki (1983)a, On the Burnside problem for periodic groups, Math. Zeitschr., 182, 385–388.
   Google Scholar
• Narain Gupta and Said Sidki, (1984), Extension of groups by tree automorphisms, Contemporary Math., 33, 232–246.
   Google Scholar
• Narain Gupta and Said Sidki, (1983)b, Some infinite p-groups, Algebra i Logika, 22, 584–589. [Russian Edition]
   Google Scholar
• Marshall Hall Jr. (1958), Solution of the Burnside problem for exponent sixsMath, III. J. Math., 2, 764–786.
   Google Scholar
• Marshall Hall Jr. (1959), The Theory of Groups, Macmillan, New York.
   Google Scholar
• Marshall Hall Jr. and Charles Sims (1982), The Burnside group of exponent 5 with two generators, Proc. Group Theory Conf., St. Andrews (1981), London Math. Soc. Lecture Notes, 71, 207–220.
   Google Scholar
• P. Hall and Graham Higman (1956), On the p-length of p-soluble groups and reduction theorems for Burnside's problem, Proc. London Math. Soc., (3) 6, 1–42.
   Google Scholar
• George Havas and M. F. Newman (1980), Applications of computers to questions like those of Burnside, Proc. Workshop on Burnside Groups, Bielefeld (1977), Lecture Notes in Math., 806 (Springer-Verlag) 211–230.
   Google Scholar
• George Havas, G. E. Wall and J. W. Wamsley (1974), The two generator restricted Burnside group of exponent five, Bull. Austral. Math. Soc., 10, 459–470.
   Google Scholar
• Graham Higman (1956), On finite groups of exponent five, Proc. Cambridge Phil Soc., 54, 1–4.
   Google Scholar
• Marshall Hall Jr. (1967), The orders of relatively free groups, Proc. Internat. Conf. Theory of Groups, Canberra (1965) Gordon & Breach, N.Y., 153–165.
   Google Scholar
• A. I. Kostrikin (1955), Solution of a weakened problem of Burnside for exponent 5, Izv. Akad. Nauk SSR Ser. Mat., 19, 233–244. [Russian]
   Google Scholar
• A. I. Kostrikin (1959), The Burnside problem, Izv. Akad. Nauk. SSSR Ser. Mat., 23, 3–34. [Russian] [Amer. Math. Soc. Transl., (2) 36 (1964), 63–99.]
   Google Scholar
• A. I. Kostrikin (1979), Sandwiches in Lie algebras. Mat. Sbornik, 110, 3–12. [Russian]
   Google Scholar
• A. I. Kostrikin (1986), Around Burnside, Nauka, Moscow. [Russian]
   Google Scholar
• A. G. Kurosh (1955), The Theory of Groups, Chelsea Publishing, N.Y.
   Google Scholar
• Friedrich Levi and B. L. van der Waerden (1933), Über eine besondere Klasse von Gruppen, Abh. Math. Sem., 9, 154–158, Univ. Hamburg.
   Google Scholar
• R. C. Lyndon (1954), On Burnside's problem, Trans. Amer. Math. Soc., 77, 202–215.
   Web of Science ®Google Scholar
• R. C. Lyndon, (1955), On Burnside's problem II, Trans. Amer. Math. Soc., 78, 329–332.
   Google Scholar
• R. C. Lyndon, (1984), Problems in combinatorial group theory, Proc. Utah Conf., Annals of Math Studies III (1987), 2–33, Princeton University Press.
   Google Scholar
• Roger C. Lyndon and Paul E. Schupp (1977), Combinatorial Group Theory, Ergeb. Math., 89, Springer-Verlag, N.Y.
   Google Scholar
• Wilhelm Magnus (1950), A connection between the Baker-Hausdorff formula and a problem of Burnside, Ann. of Math., (2) 52, 111–126.
   Web of Science ®Google Scholar
• Wilhelm Magnus, Abraham Karrass, and Donald Solitar (1966), Combinatorial Group Theory, Inter-science, N.Y.
   Google Scholar
• A. J. S. Mann (1982), On orders of groups of exponent four, J. London Math. Soc., (2) 26, 64–76.
   Google Scholar
• Yu. I. Merzlyakov (1983), Infinite finitely generated periodic groups, Dokl. Akad. Nauk SSSR, 268, 803–805. [Russian]
   Google Scholar
• M. Morse and C. A. Hedlund (1944), Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J., 11, 1–7.
   Google Scholar
• M. F. Newman (1984), Groups of exponent six, Computation Group Theory (Durham, 1982) 39–41. [Academic Press, London, New York]
   Google Scholar
• P. S. Novikov (1959), Solution of Burnside's problem on periodic groups, Uspehi Mat. Nauk, (N.S.), 14 (89) 236–237. [Russian]
   Google Scholar
• P. S. Novikov and S. I. Adian (1968), Infinite periodic groups I, II, III, Izv. Akad. Nauk SSSR Ser. Mat., 32, 212–244, 251–254, 709–731. [Russian]
   Google Scholar
• A. Ju. Ol'shanskii (1979), Infinite groups with cyclic subgroups, Dokl. Akad. Nauk SSSR, 245, 785–787. [Russian]
   Google Scholar
• A. Ju. Ol'shanskii, (1982)a, On the Novikov-Adian theorem, Math. USSR Sbornik, 46, 203–236. [Russian]
   Google Scholar
• A. Ju. Ol'shanskii (1982)b, Groups of bounded period with subgroups of prime order, Algebra i Logika, 21, 553–618.
   Google Scholar
• A. Ju. Ol'shanskii (1985), Varieties in which all finite groups are abelian, Math. Sbornik, 126 (168), 59–82 [Russian] [English transl., Math. SSSR Sbornik, 54 (1986), 57–80]
   Google Scholar
• Ju. P. Razmyslov (1978), On a problem of Hall-Higman, Izv. Akad. Nauk SSSR Ser. Mat., 42, 833–847. [Russian]
   Google Scholar
• I. N. Sanov (1940), Solution of Burnside's problem for exponent four, Leningrad Gos. Univ. Ped. Inst. Uc. Zap. Mat. Ser., 10, 166–170. [Russian]
   Google Scholar
• V. L. Shirvanian (1976), Embedding of the group B(∞, n) in the group B(2, n), Izv. Akad. Nauk SSSR Ser. Mat., 40, 190–208. [Russian]
   Google Scholar
• V. I. Sushchanskii (1979), Periodic p-groups of permutations and the unrestricted Burnside problem, Dokl. Akad. Nauk SSSR, 247, 557–561. [Russian]
   Google Scholar
• John Joseph Tobin (1954), On groups with exponent 4, Ph.D. thesis, Univ. of Manchester.
   Google Scholar
• M. R. Vaughan-Lee (1985), The restricted Burnside problem, Bull. London Math. Soc., 17, 113–133.
   Web of Science ®Google Scholar
• C. R. B. Wright (1961), On the nilpotency class of a group of exponent four, Pacific J. Math., 11, 387–394.
   Google Scholar