Equation 677 Database

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Magma af503747c088…

magma af503747c088
Size
221
Isomorphism class hash
af503747c0887636e3696e088fa891bec80fcc271b67ecc92caf19ec223cb060
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 22:20:33
Display reorder
220,168,169,170,171,173,133,138,143,148,153,123,21,26,31,36,6,11,19,50,55,65,70,75,41,46,83,88,93,98,103,113,175,172,174,158,126,0,60,108,118,208,211,202,215,179,180,181,182,176,131,136,141,146,151,120,23,28,33,38,8,13,17,53,58,68,73,78,43,48,81,86,91,96,101,111,178,183,177,156,125,3,63,106,116,205,213,201,218,190,191,184,185,187,130,135,140,145,150,121,22,27,32,37,7,10,16,52,57,67,72,77,42,47,80,85,90,95,100,110,189,186,188,155,127,2,62,105,115,206,212,200,217,192,193,194,195,197,132,137,142,147,152,122,20,25,30,35,5,12,15,51,56,66,71,76,40,45,82,87,92,97,102,112,199,196,198,157,128,1,61,107,117,207,210,204,216,160,162,163,164,166,134,139,144,149,154,124,24,29,34,39,9,14,18,54,59,69,74,79,44,49,84,89,94,99,104,114,161,165,167,159,129,4,64,109,119,209,214,203,219 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#fec06f1f4e8fb8a75710f5bc1d50e294877f11815b0f1ef2fd4a7890098a78e1, M = {44} 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 22:20:34 · history