Equation 677 Database

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Magma d630c3bd81d0…

magma d630c3bd81d0
Size
221
Isomorphism class hash
d630c3bd81d0f81cf2503c8cd8f9758cd0f6230ffd51a3106d2981571d44a97f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 220) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:03:05
Display reorder
220,191,190,184,185,186,187,188,189,11,10,9,8,31,30,29,28,50,51,49,48,74,75,73,72,95,91,90,94,114,115,113,112,130,131,128,129,151,150,148,149,215,214,213,212,196,195,197,198,199,192,193,194,12,13,6,7,32,33,26,27,53,52,46,47,69,68,66,67,88,87,85,86,110,109,107,108,132,135,127,126,152,153,147,146,210,201,208,209,179,178,180,181,182,183,176,177,5,4,3,2,25,24,23,22,44,45,43,42,64,65,63,62,93,84,83,92,105,106,104,103,124,125,122,123,145,144,142,143,207,206,205,204,163,162,164,165,166,167,161,160,0,15,14,1,20,35,34,21,55,40,54,41,71,60,70,61,89,82,80,81,111,102,101,100,134,121,120,133,141,155,140,154,200,211,202,203,175,174,168,169,170,171,172,173,19,16,17,18,39,36,37,38,56,59,57,58,78,79,76,77,96,99,97,98,116,119,117,118,136,139,138,137,159,156,158,157,219,216,217,218 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 221 = 1 + 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#9ac61f33e0de3061260327cd1f8ec493e58b27cc56b59ca78e22c7e08c8ddabf, M = {40} 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:03:06 · history