Equation 677 Database

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Magma b570ce9cadd9…

magma b570ce9cadd9
Size
231
Isomorphism class hash
b570ce9cadd9b7d55de83af29521c56f9713721bcee9c32e6bebc4dd9994a714
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 230) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 14:06:51
Display reorder
176,177,178,179,180,205,206,207,208,209,230,44,45,46,47,85,86,87,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,61,62,63,64,65,66,67,48,49,50,51,52,53,54,55,56,57,58,59,60,1,0,2,3,41,42,43,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,17,18,19,20,21,22,23,4,5,6,7,8,9,10,11,12,13,14,15,16,184,181,182,183,200,201,202,203,204,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,225,226,227,228,229,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,88,89,90,91,129,130,131,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,105,106,107,108,109,110,111,92,93,94,95,96,97,98,99,100,101,102,103,104,132,133,134,135,149,150,151,152,153,154,175,136,137,138,139,140,141,142,143,144,145,146,147,148,169,170,171,172,173,174,155,156,157,158,159,160,161,162,163,164,165,166,167,168 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 231 = 11 + 5*44, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#9dc0200dc578d1af4cb45a69ec0ee9aed85d67a2b0e70a4187efee13ed5683ab, M = {0, 1, 2, 3, 4, 29, 30, 31, 32, 33, 54} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 44): MacNeish's product over GF(4) x GF(11); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 231.

last edited by qawbecrdtey at 2026-10-06 14:06:52 · history