Equation 677 Database

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Magma 53cb7b78c84b…

magma 53cb7b78c84b
Size
221
Isomorphism class hash
53cb7b78c84b2dee8db977e4a1c365e2b6f5e6158aa922fbb373c0e635b4025c
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 21:46:15
Display reorder
220,125,120,131,136,141,146,151,156,170,171,172,173,174,175,168,169,41,45,50,55,60,65,70,75,20,25,30,35,1,5,12,15,97,102,107,112,117,82,87,92,200,211,216,205,126,121,130,135,140,145,150,155,193,194,195,196,197,198,199,192,43,48,53,58,63,68,73,78,23,28,33,38,3,8,13,19,95,100,105,110,115,81,85,90,201,213,218,206,128,123,133,138,143,148,153,158,187,188,189,190,191,184,185,186,42,47,52,57,62,67,72,77,22,27,32,37,2,7,10,16,98,103,108,113,118,83,88,93,203,212,217,207,127,122,132,137,142,147,152,157,183,176,177,178,179,180,181,182,40,46,51,56,61,66,71,76,21,26,31,36,0,6,11,18,96,101,106,111,116,80,86,91,202,210,215,208,129,124,134,139,144,149,154,159,165,166,167,161,160,162,163,164,44,49,54,59,64,69,74,79,24,29,34,39,4,9,14,17,99,104,109,114,119,84,89,94,204,214,219,209 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#05aba89c8fda3d45fa6b247c3cfa1978c014a8edff02986eef8d4cfb39f715ed, 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 21:46:16 · history