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**Generators and relations for discrete groups.**
*(English)*
Zbl 0077.02801

Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 14. Reihe: Gruppentheorie. Berlin-GĂ¶ttingen-Heidelberg: Springer-Verlag VIII, 155 S. (1957).

### Keywords:

group theory### Online Encyclopedia of Integer Sequences:

Number of groups of order n.Order of Chevalley group D_n (2).

Number of nonsingular n X n matrices over GF(2) (order of the group GL(n,2)); order of Chevalley group A_n (2); order of projective special linear group PSL_n(2).

Order of simple Chevalley group E_8(2).

Orders of Weyl groups of type E_n.

Order of universal Chevalley group A_n (3).

Order of universal Chevalley group A_n (4).

Order of universal Chevalley group A_n (5).

Order of universal Chevalley group A_n (7).

Order of universal Chevalley group A_n (8).

Order of universal Chevalley group A_n (9).

Order of (usually) simple Chevalley group A_n (3).

Order of simple Chevalley group A_n (4).

Order of simple Chevalley group A_n (5).

Order of simple Chevalley group A_n (7).

Order of simple Chevalley group A_n (8).

Order of simple Chevalley group A_n (9).

Order of universal Chevalley group A_2 (q), q = prime power.

Order of universal Chevalley group A_3 (q) (or D_3 (q)), q = prime power.

Order of universal Chevalley group A_4(q), q = prime power.

Order of universal Chevalley group A_5 (q), q = prime power.

Order of universal Chevalley group A_6(q), q = prime power.

Order of universal Chevalley group A_7 (q), q = prime power.

Order of universal Chevalley group A_8 (q), q = prime power.

Order of simple Chevalley group A_2(q), q = prime power.

Order of simple Chevalley group A_3(q) (or D_3(q)), q = prime power.

Order of simple Chevalley group A_4(q), q = prime power.

Order of simple Chevalley group A_5(q), q = prime power.

Order of simple Chevalley group A_6(q), q = prime power.

Order of simple Chevalley group A_7(q), q = prime power.

Order of simple Chevalley group A_8(q), q = prime power.

Order of universal Chevalley group D_n (3).

Order of universal Chevalley group D_n (4).

Order of universal Chevalley group D_n (5).

Order of universal Chevalley group D_n (7).

Order of universal Chevalley group D_n (8).

Order of universal Chevalley group D_n (9).

Order of (usually) simple Chevalley group D_n (3).

Order of (usually) simple Chevalley group D_n (5).

Order of (usually) simple Chevalley group D_n (7).

Order of (usually) simple Chevalley group D_n (9).

Order of universal Chevalley group D_2(q), q = prime power.

Order of universal Chevalley group D_4(q), q = prime power.

Order of universal Chevalley group D_5(q), q = prime power.

Order of universal Chevalley group D_6(q), q = prime power.

Order of universal Chevalley group D_7(q), q = prime power.

Order of universal Chevalley group D_8(q), q = prime power.

Order of (usually) simple Chevalley group D_2(q), q = prime power.

Order of simple Chevalley group D_4(q), q = prime power.

Order of simple Chevalley group D_5(q), q = prime power.

Order of simple Chevalley group D_6(q), q = prime power.

Order of simple Chevalley group D_7(q), q = prime power.

Order of simple Chevalley group D_8(q), q = prime power.

Order of universal Chevalley group B_n (3).

Order of universal Chevalley group B_n (4).

Order of universal Chevalley group B_n (5).

Order of universal Chevalley group B_n (2) or symplectic group Sp(2n,2).

Order of universal Chevalley group B_n (7).

Order of universal Chevalley group B_n (8).

Order of universal Chevalley group B_n (9).

Order of universal Chevalley group B_2(q), q = prime power.

Order of universal Chevalley group B_3(q), q = prime power.

Order of universal Chevalley group B_4(q), q = prime power.

Order of universal Chevalley group B_5(q), q = prime power.

Order of universal Chevalley group B_6(q), q = prime power.

Order of universal Chevalley group B_7(q), q = prime power.

Order of universal Chevalley group B_8(q), q = prime power.

Order of (usually) simple Chevalley group B_2(q), q = prime power.

Order of simple Chevalley group B_3(q), q = prime power.

Order of simple Chevalley group B_4(q), q = prime power.

Order of simple Chevalley group B_5(q), q = prime power.

Order of simple Chevalley group B_6(q), q = prime power.

Order of simple Chevalley group B_7(q), q = prime power.

Order of simple Chevalley group B_8(q), q = prime power.

Exponents m_i associated with Weyl group W(E6).

Exponents m_i associated with Weyl group W(E7).

Exponents m_i associated with Weyl group W(E_8).

Degrees of fundamental invariants of Weyl group W(E6).

Degrees of fundamental invariants of Weyl group W(E7).

Degrees of fundamental invariants of Weyl group W(E_8).

Molien series for Weyl group E_7.

Molien series for 4-dimensional reflection group [3,3,5] of order 14400.

Order of simple Chevalley group E_8 (q), q = prime power.

Order of universal Chevalley group E_7 (q), q = prime power.

Order of simple Chevalley group E_7 (q), q = prime power.

Order of universal Chevalley group E_6 (q), q = prime power.

Order of simple Chevalley group E_6 (q), q = prime power.

Order of simple Chevalley group F_4(q), q = prime power.

Order of simple Chevalley group G_2 (q), q = prime power.

Number of words of length 2n generated by the two letters s and t that reduce to the identity 1 using the relations sssssss=1, tt=1 and stst=1. The generators s and t along with the three relations generate the 14-element dihedral group D7.

Numbers n such that 30*n+{1,7,11,13,17,19,23,29} are all composite.

Number of reduced words of length n in the Weyl group E_7 on 7 generators and order 2903040.

Number of reduced words of length n in the Weyl group E_8 on 8 generators and order 696729600.

Number of reduced words of length n in the icosahedral reflection group [3,5] of order 120.

Number of reduced words of length n in the reflection group [3,4,3] of order 1152.

Number of reduced words of length n in the reflection group [3,3,5] of order 14400.

Non-Abelian numbers: n such that A000001(n)/A000688(n) is a new record.

The growth series for the affine Coxeter (or Weyl) group [3,5] (or H_3).

The growth series for the affine Coxeter (or Weyl) group [3,3,5] (or H_4).

The growth series for the affine Weyl group F_4.

The growth series for the affine Weyl group E_7.

The growth series for the affine Weyl group E_8.

Degrees of fundamental invariants of Weyl group W(E_6).