[AL]
Adams, William W. and Loustaunau, Philippe. An introduction to Gröbner bases. Graduate Studies in Mathematics 3 (American Mathematical Society, Providence
1994).

[AM]
Atiyah, M. F. and Macdonald, I. G.
Introduction to Commutative Algebra (Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969), ix+128 pp.

[Ber]
Bergeron, F.
Algebraic combinatorics and coinvariant spaces. CMS Treatises in Mathematics. Canadian Mathematical Society, Ottawa, ON (A K Peters, Ltd., Wellesley, MA, 2009), viii+221.

[Bou]
Bourbaki, N.
Elements of Mathematics: Algebra I (Addison-Wesley, 1974).

[Br]
Brauer, R.
Representations of finite groups. Lectures in Modern Mathematics, vol. I, Editor Saaty, T. L. (Wiley, New York, 1963), 133–175.

[Cur]
Curtis, C. W.
Pioneers of representation theory: Frobenius, Burnside, Schur and Brauer. History of Mathematics **15** (American Mathematical Society, Providence, RI; London Mathematical Society, London, 1999), 287 pages.

[FS]
Formanek, E. and Sibley, D.
The group determinant determines the group. Proc. Amer. Math. Soc.
112 (1991), 649–656.

[Fr]
Frobenius, F.G. Über vertauschbare Matrizen. *S'ber. Akad. Wiss. Berlin* (1896), 601–614.

[Ge]
Gerstenhaber, M.
On nilalgebras and linear varieties of nilpotent matrices. III.
Ann. of Math. (2) 70 (1959) 167–205.

[G]
Göbel, M.
Computing bases for rings of permutation-invariant polynomials. J. Symbolic Comput.
19 (1995), no. 4, 285–291.

[Gr]
Grigorchuk, R. I.
*Symmetrical random walks on discrete groups*
. Multicomponent random systems, pp. 285-325. Adv. Probab. Related Topics, **6** (Dekker, New York, 1980).

[GB]
Grove, L. C. and Benson, C. T.
Finite reflection groups. Second edition. Graduate Texts in Mathematics, **99** (Springer-Verlag, New York, 1985). x+133 pp.

[HoJ]
Hoehnke, H.-J. and Johnson, K. W.. 3-characters are sufficient for the group determinant. Second International Conference on Algebra (Barnaul, 1991)), 193–206. Contemp. Math.
**184** (Amer. Math. Soc., Providence, RI, 1995).

[Hul]
Hulek, K.
Elementary algebraic geometry. Translated from the 2000 German original by Helena Verrill. Student Mathematical Library, 20 (American Mathematical Society, Providence, RI, 2003). viii+213 pp.

[Hu]
Humphries, S. P.
Cogrowth of groups and the Dedekind–Frobenius group determinant. Math. Proc. Camb. Phil. Soc.
121 (1997), 193–217.

[HR]
Humphries, S. P. and Rode, E. L.
*Weak Cayley tables and generalised centraliser rings of finite groups*. To appear in *Math Proc. Camb. Phil. Soc.* (2012).

[HJM]
Humphries, S. P., Johnson, K. W. and Misseldine, A. Commutative *S*-rings of maximal dimension, preprint (2013).

[Isa]
Isaacs, I. M.
Finite group theory. Graduate Studies in Mathematics, 92 (American Mathematical Society, Providence, RI, 2008). xii+350 pp.

[Ja]
Jantzen, J. C.
Nilpotent orbits in representation theory. Lie theory, 1-211. Progr. Math.
**228** (Birkhuser Boston, Boston, MA, 2004).

[J]
Johnson, K. W. On the group determinant. Math. Proc. Camb. Phil. Soc.
109 (1991), 299–311.

[Ke]
Keller, J. Representations associated to the group matrix. MS thesis. Brigham Young University (2014), 45 pages.

[Kou]
Kouksov, D.
On rationality of the cogrowth series. Proc. Amer. Math. Soc.
126 (1998), 2845–2847.

[L]
Lam, T. Y.
Representations of finite groups: a hundred years. I. Not. Amer. Math. Soc.
45 (1998), no. 3, 361–372.

[Mac]
Macdonald, I. G.
Symmetric functions and Hall polynomials. Second edition. With contributions by A. Zelevinsky. Oxford Mathematical Monographs. Oxford Science Publications. (The Clarendon Press, Oxford University Press, New York, 1995).

[MA]
Bosma, W. and Cannon, J.
MAGMA (University of Sydney, 1994).

[Man]
Mansfield, R.
A group determinant determines its group. Proc. Amer. Math. Soc.
116 (1992), 939–941.

[Mil]
Milnor, J.
Singular points of complex hypersurfaces. Annals of Math. Stud., No. 61 (Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo
1968), iii+122 pp.

[OV]
Okounkov, A. and Vershik, A.
A new approach to representation theory of symmetric groups. Selecta Math. (N.S.) 2 (1996), no. 4, 581–605.

[Rod]
Rode, E. The 3-S-ring determines a finite group. Preprint (2012).

[R]
Roggenkamp, K. W.
From Dedekind's group determinant to the isomorphism problem. C. R. Math. Acad. Sci. Soc. R. Can.
21 (1999), 97–126.

[Sch]
Schur, I.
Zur Theorie der einfach transitiven Permutationsgruppen. Sitz. Preuss. Akad. Wiss. Berlin, Phys-math Klasse (1933), 598–623.

[Sc]
Scott, W. R.
Group theory (Dover, 1987).

[Sk]
Skrzyński, M.
On basic geometric properties of the cones of nilpotent matrices. Univ. Iagel. Acta Math. No. 33 (1996), 219–228.

[St1]
Stanley, R. P.
Hilbert functions of graded algebras. Advances in Math.
28 (1978), no. 1, 57–83.

[St2]
Stanley, R. P.
Invariants of finite groups and their applications to combinatorics. Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 3, 475–511.

[St]
Sturmfels, B.
Algorithms in invariant theory. Second edition. Texts and Monographs in Symbolic Computation. (Springer Wien New York, Vienna, 2008), vi+197 p.

[VZ]
Vyshnevetskiy, A. L. and Zhmud, E. M.
Random walks on finite groups converging after finite number of steps. Algebra Discrete Math. (2008), no. 2, 123–129.

[Wie]
Helmut, W.
Zur theorie der einfach transitiven permutationsgruppen II. Math. Z.
52 (1949), 384–393.

[Wo]
Woess, W.
Cogrowth of groups and simple random walks. Arch. Math. (Basel) 41 (1983), no. 4, 363–370.