Bulletin of the American Mathematical Society

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Book Information:

Author: Yakov Berkovich
Title: Groups of prime power order. Vol. 1 (with a foreword by Zvonimir Janko)
Additional book information: de Gruyter Expositions in Mathematics, 46, Walter de Gruyter GmbH \& Co. KG, Berlin, 2008, xx+512 pp., ISBN 978-3-11-020418-6

Author: Yakov Berkovich and Zvonimir Janko
Title: Groups of prime power order. Vol. 2
Additional book information: de Gruyter Expositions in Mathematics, 47, Walter de Gruyter GmbH \& Co. KG, Berlin, 2008, xvi+596 pp., ISBN 978-3-11-020419-3

S. I. Adian, The Burnside problem and identities in groups, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 95, Springer-Verlag, Berlin-New York, 1979. Translated from the Russian by John Lennox and James Wiegold. MR 537580

Hans Ulrich Besche, Bettina Eick, and E. A. O’Brien, A millennium project: constructing small groups, Internat. J. Algebra Comput. 12 (2002), no. 5, 623–644. MR 1935567, DOI 10.1142/S0218196702001115

Simon R. Blackburn, Peter M. Neumann, and Geetha Venkataraman, Enumeration of finite groups, Cambridge Tracts in Mathematics, vol. 173, Cambridge University Press, Cambridge, 2007. MR 2382539, DOI 10.1017/CBO9780511542756

M. R. Bridson. Decision problems and profinite completions of groups. J. Algebra (to appear).

R. M. Bryant and L. G. Kovács, Lie representations and groups of prime power order, J. London Math. Soc. (2) 17 (1978), no. 415-421. MR 506776, DOI 10.1112/jlms/s2-17.3.415

Bettina Eick, Automorphism groups of 2-groups, J. Algebra 300 (2006), no. 1, 91–101. MR 2228637, DOI 10.1016/j.jalgebra.2006.01.024

Bettina Eick and Charles Leedham-Green, On the classification of prime-power groups by coclass, Bull. Lond. Math. Soc. 40 (2008), no. 2, 274–288. MR 2414786, DOI 10.1112/blms/bdn007

Marcus du Sautoy, Counting $p$-groups and nilpotent groups, Inst. Hautes Études Sci. Publ. Math. 92 (2000), 63–112 (2001). MR 1839487

Wolfgang Gaschütz, Nichtabelsche $p$-Gruppen besitzen äussere $p$-Automorphismen, J. Algebra 4 (1966), 1–2 (German). MR 193144, DOI 10.1016/0021-8693(66)90045-7

Narain Gupta, The dimension subgroup conjecture, Bull. London Math. Soc. 22 (1990), no. 5, 453–456. MR 1082014, DOI 10.1112/blms/22.5.453

P. Hall. A contribution to the theory of groups of prime power order. Proc. London Math. Soc. 36 (1933), 29–95.

Marshall Hall Jr. and James K. Senior, The groups of order $2^{n}\,(n\leq 6)$, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1964. MR 0168631

Graham Higman, Enumerating $p$-groups. II. Problems whose solution is PORC, Proc. London Math. Soc. (3) 10 (1960), 566–582. MR 123605, DOI 10.1112/plms/s3-10.1.566

D. R. Hughes. A research problem in group theory. Bull. Amer. Math. Soc. 63 (1957), 209.

D. R. Hughes and J. G. Thompson, The $H$-problem and the structure of $H$-groups, Pacific J. Math. 9 (1959), 1097–1101. MR 108532

B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703

E. I. Khukhro, $p$-automorphisms of finite $p$-groups, London Mathematical Society Lecture Note Series, vol. 246, Cambridge University Press, Cambridge, 1998. MR 1615819, DOI 10.1017/CBO9780511526008

Evgenii I. Khukhro, Nilpotent groups and their automorphisms, De Gruyter Expositions in Mathematics, vol. 8, Walter de Gruyter & Co., Berlin, 1993. MR 1224233, DOI 10.1515/9783110846218

Michel Lazard, Groupes analytiques $p$-adiques, Inst. Hautes Études Sci. Publ. Math. 26 (1965), 389–603 (French). MR 209286

Alexander Lubotzky and Avinoam Mann, Powerful $p$-groups. I. Finite groups, J. Algebra 105 (1987), no. 2, 484–505. MR 873681, DOI 10.1016/0021-8693(87)90211-0

E. A. O’Brien, The $p$-group generation algorithm, J. Symbolic Comput. 9 (1990), no. 5-6, 677–698. Computational group theory, Part 1. MR 1075431, DOI 10.1016/S0747-7171(08)80082-X

E. A. O’Brien and M. R. Vaughan-Lee, The groups with order $p^7$ for odd prime $p$, J. Algebra 292 (2005), no. 1, 243–258. MR 2166803, DOI 10.1016/j.jalgebra.2005.01.019

E. A. O’Brien and Michael Vaughan-Lee, The 2-generator restricted Burnside group of exponent 7, Internat. J. Algebra Comput. 12 (2002), no. 4, 575–592. MR 1919689, DOI 10.1142/S0218196702001103

Mohamed A. M. Salim and Robert Sandling, The modular group algebra problem for groups of order $p^5$, J. Austral. Math. Soc. Ser. A 61 (1996), no. 2, 229–237. MR 1405536

Aner Shalev, The structure of finite $p$-groups: effective proof of the coclass conjectures, Invent. Math. 115 (1994), no. 2, 315–345. MR 1258908, DOI 10.1007/BF01231763

Charles C. Sims, Computation with finitely presented groups, Encyclopedia of Mathematics and its Applications, vol. 48, Cambridge University Press, Cambridge, 1994. MR 1267733, DOI 10.1017/CBO9780511574702

M. R. Vaughan-Lee, Lie rings of groups of prime exponent, J. Austral. Math. Soc. Ser. A 49 (1990), no. 3, 386–398. MR 1074510

Michael Vaughan-Lee, The restricted Burnside problem, 2nd ed., London Mathematical Society Monographs. New Series, vol. 8, The Clarendon Press, Oxford University Press, New York, 1993. MR 1364414

G. E. Wall, On Hughes’ $H_{p}$ problem, Proc. Internat. Conf. Theory of Groups (Canberra, 1965) Gordon and Breach, New York, 1967, pp. 357–362. MR 0219607

Bettina Wilkens, On quaternion-free 2-groups, J. Algebra 258 (2002), no. 2, 477–492. MR 1943930, DOI 10.1016/S0021-8693(02)00638-5

E. I. Zel′manov, Solution of the restricted Burnside problem for groups of odd exponent, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), no. 1, 42–59, 221 (Russian); English transl., Math. USSR-Izv. 36 (1991), no. 1, 41–60. MR 1044047

E. I. Zel′manov, Solution of the restricted Burnside problem for $2$-groups, Mat. Sb. 182 (1991), no. 4, 568–592 (Russian); English transl., Math. USSR-Sb. 72 (1992), no. 2, 543–565. MR 1119009

• S. I. Adian, The Burnside problem and identities in groups. Translated from the Russian by J. Lennox and J. Wiegold. Ergebnisse der Mathematik und ihrer Grenzgebiete, 95, Springer, Berlin, 1979. MR 537580 (80d:20035)
• H. U. Besche, B. Eick, and E. A. O’Brien. A millennium project: constructing small groups. Intern. J. Comput. 12(5) (2002), 623–644. MR 1935567 (2003h:20042)
• S. R. Blackburn, P. M. Neumann, and G. Venkataraman. Enumeration of finite groups. Cambridge Tracts in Mathematics, 173. Cambridge University Press, Cambridge, 2007. MR 2382539 (2009c:20041)
• M. R. Bridson. Decision problems and profinite completions of groups. J. Algebra (to appear).
• R. M. Bryant and L. G. Kovács. Lie representations and groups of prime power order. J. London Math. Soc. 17 (1978), 415–421. MR 0506776 (58:22263)
• B. Eick. Automorphism groups of $2$-groups. J. Algebra 300 (2006), 91–101. MR 2228637 (2007f:20039)
• B. Eick and C. R. Leedham-Green. On the classification of prime-power groups by coclass. Bull. London Math. Soc. 40(2) (2008), 274–288. MR 2414786 (2009b:20030)
• M. du Sautoy. Counting $p$-groups and nilpotent groups. Inst. Hautes Études Sci. Publ. Math. 92 (2001), 63–112. MR 1839487 (2002f:11122)
• W. Gaschütz. Nicht abelsche $p$-Gruppen besitzen äußere $p$-Automorphismen. J. Algebra 4 (1966), 1–2. MR 0193144 (33:1365)
• N. Gupta. The dimension subgroup conjecture. Bull. London Math. Soc. 22(5) (1990), 453–456. MR 1082014 (92d:20009)
• P. Hall. A contribution to the theory of groups of prime power order. Proc. London Math. Soc. 36 (1933), 29–95.
• M. Hall and J. K. Senior. The groups of order $2^n$ $(n\le 6)$. Macmillan, New York, 1964. MR 0168631 (29:5889)
• G. Higman. Enumerating $p$-groups II: Problems whose solution is PORC. Proc. London Math. Soc. 10 (1960), 566–582. MR 0123605 (23:A930)
• D. R. Hughes. A research problem in group theory. Bull. Amer. Math. Soc. 63 (1957), 209.
• D. R. Hughes and J. G. Thompson. The $\mathrm {H}_p$ problem and the structure of $\mathrm {H}_p$-groups. Pacific J. Math. 9 (1959), 1097–1101. MR 0108532 (21:7248)
• B. Huppert, Endliche Gruppen I. Springer, Berlin, 1967. MR 0224703 (37:302)
• E. I. Khukhro. $p$-automorphisms of finite $p$-groups. London Mathematical Society Lecture Note Series 246, Cambridge University Press, Cambridge, 1997. MR 1615819 (99d:20029)
• E. I. Khukhro. Nilpotent groups and their automorphisms. De Gruyter Expositions in Mathematics 8, De Gruyter, Berlin, New York, 1993. MR 1224233 (94g:20046)
• M. Lazard. Groupes analytiques $p$-adiques. Publ. Math. IHES 26 (1965), 389–603. MR 0209286 (35:188)
• A. Lubotzky and A. Mann. Powerful $p$-groups. I: finite groups. J. Algebra 105 (1987), 484–505; II: $p$-adic analytic groups. J. Algebra 105 (1987), 506–515. MR 873681 (88f:20045)
• E. A. O’Brien. The $p$-group generation program. J. Symbolic Comp. 9 (1990), 677–698. MR 1075431 (91j:20050)
• E. A. O’Brien and M. R. Vaughan-Lee. The groups of order $p^7$ for odd prime $p$. J. Algebra 292(1) (2005), 243–258. MR 2166803 (2006d:20038)
• E. A. O’Brien and M. R. Vaughan-Lee. The $2$-generator restricted Burnside group of exponent $7$. Internat. J. Algebra Comput. 12(4) (2002), 575–592. MR 1919689 (2003i:20032)
• M. A. M. Salim and R. Sandling. The modular group algebra problem for groups of order $p^5$. J. Austral. Math. Soc. (Series A) 61 (1996), 229–237. MR 1405536 (97e:16064)
• A. Shalev. The structure of finite $p$-groups: effective proof of the coclass conjectures. Invent. Math. 115 (1994), 315–345. MR 1258908 (95j:20022b)
• C. C. Sims. Computation with finitely presented groups. Encyclopedia of Mathematics and Its Applications 48. Cambridge University Press, Cambridge, 1994. MR 1267733 (95f:20053)
• M. Vaughan-Lee. Lie rings of groups of prime exponent. J. Austral. Math. Soc. 49 (1990), 386–398. MR 1074510 (91m:20059)
• M. Vaughan-Lee. The restricted Burnside problem. Oxford University Press. Second Edition, 1993. MR 1364414 (98b:20047)
• G. E. Wall. On Hughes’ $\mathrm {H}_p$-problem, 1967 Proc. Internat. Conf. Theory of Groups (Canberra, 1965). Lecture Notes in Math. 372. Springer, 1974, 667–690. MR 0219607 (36:2686)
• B. Wilkens. On quaternion-free $2$-groups. J. Algebra 258 (2002), 477–492. MR 1943930 (2003i:20033)
• E. Zelmanov. Solution of the restricted Burnside problem for groups of odd exponent. Izv. Akad. Nauk SSSR Ser. Mat. 54 (1991), 42–59. MR 1044047 (91i:20037)
• E. Zelmanov. Solution to the restricted Burnside problem for $2$-groups. Mat. Sb. 182(4) (1991), 568–592. MR 1119009 (93a:20063)