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References for the GroupTheory package

A large number of print and web resources were consulted during the construction of the GroupTheory package. The most relevant general references are listed here. We also gratefully acknowledge contributions by the Computer Algebra Group at Simon Fraser University; in particular work by Vahid Dabbaghian, Michael Monagan and Asif Zaman.


Print Resources

Web Resources

Print Resources

Amiri, H. and S. M. Jafarian Amiri, Sum of element orders on finite groups of the same order, Journal of Algebra and its Applications 10 (No. 2), 2011, 187 - 190.

M. D. Atkinson (Ed.), Computational Group Theory, Proceedings of the London Mathematical Society Symposium on Computational Group Theory, Academic Press, London, 1984.

T. R. Berger, A Converse to Lagrange's Theorem, J. Austral. Math. Soc. 15 (Ser. A) (1978), 291 - 313.

David Burrell, On the number of groups of order 1024, Comm. Algebra 50 (No. 6) 2022, 2038-2010.

David Burrell, The number of _p_-groups of order _19,683_ and new lists of _p_-groups Comm. Algebra 51 (No. 6) 2023, 2673-2679.

David Burrell, Computation of Finite Groups, Ph. D. Thesis, University of Florida, 2023.

G. Butler, Fundamental Algorithms for Permutation Groups, Lecture Notes in Computer Science 559, Springer-Verlag, Heidelberg, 1991.

R. Carter, Simple Groups and Simple Lie Algebras, J. London Math. Soc. 40 (1966), 193-240.

R. Carter, Simple Groups of Lie Type, Wiley, New York, 1972.

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985.

B. N. Cooperstein, Minimal degree for a permutation representation of a classical group, Israel J. Math. 30, No. 3 (1978), 213 - 235.

Rex Dark and Carlo M. Scoppola, On Camina groups of prime power order, J. Algebra 181 (1996), 878 - 802.

Constance Davis, A Bibliographical Survey of Simple Groups of Finite Order: 1900-1965, Courant Institute of Mathematical Sciences, New York University, 1969.

Bettina Eick, Enumeration of groups whose order factorises in at most 4 primes, arxiv:1702.02616v1 [math.GR], 2017, at

Bettina Eick and Max Horn, The Construction of finite solvable groups revisited, J. Algebra 408 (2014), 166-182.

Bettina Eick and Tobias Moede, The enumeration of groups of order __p^n*q__ for __n <= 5__ J. Algebra 507 (2018), 571-591.

A. G. Earnest, R. A. Catalpa, U. S. Schmidt and G. T. Stewart, Remarks on the Generation of Orthogonal Groups over Finite Fields, J. Algebra 176 (1995), 585 - 590.

W. Feit, H. Hall, Jr. and J.G. Thompson, Finite groups in which the centralizer of any non-identity element is nilpotent, Math. Z. 74 (1960), 1 - 17.

Marshall Hall and L. J. Paige, Complete mappings of finite groups, Pacific J. Math. 5 (1955), 541 - 549.

Marcel Herzog, Patrizia Longobardi and Mercede Maj, Another criterion for solvability of finite groups, J. Algebra 597 (2022), 1 - 23.

Derek F. Holt, Bettina Eick and Eamonn A. O'Brien, Handbook of Computational Group Theory. Chapman & Hall/CRC Press, Boca Raton, 2005.

Derek F. Holt and W. Plesken, Perfect Groups, Oxford Math. Monographs, Oxford University Press, 1989.

Hiroyuki Ishibashi and A. G. Earnest, Two-Element Generation of Orthogonal Groups over Finite Fields, J. Algebra 165 (1994), 164 - 171. (Erratum, J. Algebra 170 (1994) 1035.)

Naihan Jing, The order of groups satisfying a converse to Lagrange's theorem, Mathematika 47 (2000), 107 - 204.

Kenneth W. Johnson, Group Matrices, Group Determinants and Representation Theory: The mathematical legacy of Frobenius, Lecture Notes in Mathematics 2233, Springer Nature, Switzerland, 2019.

William M. Kantor, Finding composition factors of permutation groups of degree _<= 10^6_, J. Symb. Comp. 12 (1991), 517 - 526.

Wolfgang Kimmerle, Richard Lyons, Robert Sandling and David N. Teague, Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups, Proc. London Math. Soc. (3) 60 (1990), 89 - 122.

MacDonald, I.G., Numbers of Conjugacy Classes in some Finite Classical Groups, Bull. Austral. Math. Soc. 23 (1981), 23 - 48.

Yadollah Marefat, Ali Iranmanesh and Abolfazl Tehranian, On The Sum Of Element Orders Of Finite Simple Groups, J. Algebra. Appl. 12 (No. 7), 2013,

Klaus Lux and Herbert Pahlings, Representations of Groups: A Computational Approach. Cambridge Studies in advanced mathematics, 124. Cambridge University Press, Cambridge, UK, 2010.

J. Neubüser, Untersuchungen des Untergruppenverbandes endlicher Gruppen auf einer programmgesteuerten elektronischen Dualmaschine, Numerische Mathematik 2, pp. 280-292, Springer-Verlag, Heidelberg, 1960.

J. Pazderski, Die Ordnungen, zu denen nur Gruppen mit gegebener Eigenschaft gehören, Arch. Math. 10 (1959), Issue 1, pp. 331–343.

Derek J. S. Robinson, A Course in the Theory of Groups, Graduate Texts in Mathematics 80, Springer-Verlag, New York, 1993.

John S. Rose, Finite groups with prescribed Sylow tower subgroups, Proc. London Math. Soc. (3) 16, (1966), 577-589.

Ákos Seress, Permutation Group Algorithms, Cambridge Tracts in Mathematics 152, Cambridge University Press, Cambridge (UK), 2003.

Michio Suzuki, The nonexistence of a certain type of simple groups of odd order, Proc. Amer. Math. Soc. 8 (1957), 686 - 695.

D. E. Taylor, Pairs of Generators for Matrix Groups, I, The Cayley Bulletin, No. 3, Oct. 1987, 76 - 85. arxiv:2201.09155v1 [math.GR], 2022, at

John G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74 (1968), 383-437.

G. E. Wall, On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Austral. Math. Soc. 3 (1963), 1 - 62.

L. Weisner, Groups in which the normalizer of every element except the identity is abelian, Bull, Amer. Math. Soc. 31 (1925), 413 - 416.

Robert A. Wilson, The Finite Simple Groups, Graduate Texts in Mathematics 251, Springer-Verlag, London, 2009.

Web Resources

H.U. Besche, B. Eick and E. O'Brien, The Small Groups library, 2002, at

Robert Wilson, Peter Walsh, Jonathan Tripp, Ibrahim Suleiman, Richard Parker, Simon Norton, Simon Nickerson, Steve Linton, John Bray and Rachel Abbott, Atlas of Finite Group Representations at