Equation 677 Database

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Magma 6a46ca4f3a67…

magma 6a46ca4f3a67
Size
221
Isomorphism class hash
6a46ca4f3a676d777f27f6abe4b725f903191f9c9dba1bab889babc29c11a97b
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 22:20:24
Display reorder
220,24,29,34,39,9,49,54,59,64,69,79,139,144,149,154,124,129,134,175,168,170,171,172,173,174,99,104,109,114,119,89,18,4,14,74,44,159,169,84,94,214,208,204,219,20,25,30,35,5,46,51,56,61,66,76,135,140,145,150,120,125,130,189,190,184,185,186,187,188,96,101,106,111,116,86,15,0,12,71,41,155,191,80,91,211,205,200,218,21,26,31,36,6,45,50,55,60,65,75,137,142,147,152,122,127,132,194,195,197,198,199,192,193,97,102,107,112,117,87,19,1,11,70,40,157,196,82,92,210,206,202,216,23,28,33,38,8,48,53,58,63,68,78,138,143,148,153,123,128,133,165,166,161,160,162,163,164,98,103,108,113,118,88,17,3,13,73,43,158,167,83,93,213,207,203,217,22,27,32,37,7,47,52,57,62,67,77,136,141,146,151,121,126,131,180,181,183,176,177,178,179,95,100,105,110,115,85,16,2,10,72,42,156,182,81,90,212,209,201,215 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 = {41} 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 22:20:25 · history