In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H 2 ( G , Z ) {\displaystyle H_{2}(G,\mathbb {Z}...

perfect but has a Schur multiplier that is larger than expected include: A1(4) The Schur multiplier has an extra Z/2Z, so the Schur multiplier of the simple...

all finite simple groups, together with their order, the size of the Schur multiplier, the size of the outer automorphism group, usually some small representations...

mathematical field of representation theory, a Herz–Schur multiplier (named after Carl S. Herz and Issai Schur) is a special kind of mapping from a group to...

cover. In these cases, then, the Schur multiplier is (the cyclic group) of order 6. These were first computed in (Schur 1911). H2(An, Z) = Z1 for n = 1...

Schur. Frobenius–Schur indicator Herz–Schur multiplier Jordan–Schur theorem Lehmer–Schur algorithm Schur algebra Schur class Schur's conjecture Schur...

product: ch. 5  or Schur product) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding...

of Lie type, it is sometimes regarded as a 27th sporadic group. The Schur multiplier of the Tits group is trivial and its outer automorphism group has order 2...

the 4-group. The second homology groups, known classically as the Schur multipliers, were computed in (Ihara & Yokonuma 1965). They are: H 2 ( C n , Z...

exceptional Schur multiplier (a triple cover) and that these extend to triple covers of S6 and S7, these do not correspond to exceptional Schur multipliers of...

after Issai Schur: List of things named after Issai Schur Schur algebra Schur complement Schur index Schur indicator Schur multiplier Schur orthogonality...

in terms of the first homology group of W {\displaystyle W} . The Schur multiplier M ( W ) {\displaystyle M(W)} , equal to the second homology group of...

cohomology Group extension Presentation of a group Product of group subsets Schur multiplier Semidirect product Sylow theorems Hall subgroup Wreath product Butterfly...

Algebra, Galois Theory, Representation Theory, Group Extensions and Schur Multiplier (Berlin, Heidelberg: Springer, 2017), p. 206. "Abel Prize Awarded:...

The Schur complement of a block matrix, encountered in linear algebra and the theory of matrices, is defined as follows. Suppose p, q are nonnegative...

all such homomorphisms, this D has maximal size. The Schur multiplier of G is the kernel of any Schur cover and has many interpretations. When the homomorphism...

p. ix. ISBN 978-0-582-02693-3. J. W. Davies and A. O. Morris, "The Schur Multiplier of the Generalized Symmetric Group", J. London Math. Soc. (2), 8, (1974)...

monster group. The outer automorphism group of B is trivial and the Schur multiplier of B has order 2. The existence of this group was suggested by Bernd...

theorems Hall's theorem p-group Elementary abelian group Frobenius group Schur multiplier Classification of finite simple groups cyclic alternating Lie type...

A008915 in the OEIS). The Schur multiplier of E6(q) is always gcd(3,q−1) (i.e., E6,sc(q) is its Schur cover). The Schur multiplier of 2E6(q) is gcd(3,q+1)...

Fischer group Fi24, the baby monster, and the Conway group Co1. The Schur multiplier and the outer automorphism group of the monster are both trivial. The...

theorems Hall's theorem p-group Elementary abelian group Frobenius group Schur multiplier Classification of finite simple groups cyclic alternating Lie type...

circle SO(2) / {±1} is a maximal compact subgroup of PSL(2, R). The Schur multiplier of the discrete group PSL(2, R) is much larger than Z, and the universal...

In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the...

existence of a complement in Schur's published works, though the results of Schur (1904, 1907) on the Schur multiplier imply the existence of a complement...

theorems Hall's theorem p-group Elementary abelian group Frobenius group Schur multiplier Classification of finite simple groups cyclic alternating Lie type...

split. For the Higman-Sims group, n = 2 and the extension splits. The Schur multiplier has order 3, and its outer automorphism group has order 2. (Griess...

theorems Hall's theorem p-group Elementary abelian group Frobenius group Schur multiplier Classification of finite simple groups cyclic alternating Lie type...

theorems Hall's theorem p-group Elementary abelian group Frobenius group Schur multiplier Classification of finite simple groups cyclic alternating Lie type...

which are the Schur multipliers of the symmetric group and signed symmetric group. Davies, J. W.; Morris, A. O. (1974), "The Schur Multiplier of the Generalized...