Equation 677 Database

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Magma 7bb159a8fbe3…

magma 7bb159a8fbe3
Size
221
Isomorphism class hash
7bb159a8fbe35ac527e735c28a766d2c7e09db4386dfdb91d342533cddfc8537
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 22:14:32
Display reorder
220,1,35,5,12,15,20,25,30,75,40,48,50,55,60,65,70,122,127,132,137,142,147,152,157,162,163,164,165,166,167,161,160,85,90,95,101,106,111,116,80,200,212,206,216,3,38,8,13,17,23,28,33,78,43,47,53,58,63,68,73,120,126,131,136,141,146,151,156,170,171,172,173,174,175,168,169,86,91,96,100,105,110,115,81,201,213,205,218,2,37,7,10,16,22,27,32,77,41,46,52,57,62,67,72,121,125,130,135,140,145,150,155,181,182,183,176,177,178,179,180,87,92,97,102,107,112,117,82,202,211,209,217,0,36,6,11,19,21,26,31,76,42,45,51,56,61,66,71,123,128,133,138,143,148,153,158,184,185,186,187,188,189,190,191,88,93,98,103,108,113,118,83,203,210,207,215,4,39,9,14,18,24,29,34,79,44,49,54,59,64,69,74,124,129,134,139,144,149,154,159,194,195,196,197,198,199,192,193,89,94,99,104,109,114,119,84,204,214,208,219 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#a97cd359209ca8128895583745774fa637e4d6ff9668d716e70c1186faf8de63, 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 22:14:33 · history