Equation 677 Database

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Magma 149def47d67b…

magma 149def47d67b
Size
221
Isomorphism class hash
149def47d67be6c661a8ab9035204cca4af58093cc0a1a03e911a64e0921a543
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 22:20:30
Display reorder
220,139,144,149,154,124,109,114,119,84,89,99,162,163,164,165,167,161,160,49,54,64,69,74,79,44,24,29,34,39,4,14,134,159,129,94,104,166,59,9,18,209,218,214,204,138,143,148,153,123,108,113,118,83,88,98,186,187,188,189,191,184,185,47,52,62,67,72,77,42,22,27,32,37,1,10,133,158,128,93,103,190,57,6,16,207,219,211,203,135,140,145,150,121,107,112,117,82,87,97,198,199,192,193,195,196,197,48,53,63,68,73,78,43,23,28,33,38,3,13,130,155,125,92,102,194,58,8,17,205,217,213,201,137,142,147,152,122,105,110,115,81,86,96,170,171,172,173,175,168,169,46,51,61,66,71,76,40,20,25,30,35,0,11,132,157,127,91,101,174,56,5,19,208,215,210,202,136,141,146,151,120,106,111,116,80,85,95,182,183,176,177,179,180,181,45,50,60,65,70,75,41,21,26,31,36,2,12,131,156,126,90,100,178,55,7,15,206,216,212,200 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 = {43} 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 22:20:31 · history