Equation 677 Database

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Magma 72c8388f9c6f…

magma 72c8388f9c6f
Size
221
Isomorphism class hash
72c8388f9c6f9d6ec000022ba20442db090b3d46a5386f53cc01ffb8bbecebec
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 21:46:19
Display reorder
220,48,43,53,58,63,68,73,78,151,156,121,126,131,136,141,146,110,115,81,85,90,95,100,105,33,38,3,8,13,15,23,28,195,196,197,198,199,192,193,194,213,201,218,206,46,41,51,56,61,66,71,75,150,155,120,125,130,135,140,145,112,117,82,87,92,97,102,107,31,35,1,5,10,19,21,26,168,169,170,171,172,173,174,175,211,202,216,205,47,42,52,57,62,67,72,77,153,158,123,128,133,138,143,148,113,118,83,88,93,98,103,108,32,37,2,7,12,17,22,27,188,189,190,191,184,185,186,187,212,203,217,207,49,44,54,59,64,69,74,79,154,159,124,129,134,139,144,149,114,119,84,89,94,99,104,109,34,39,4,9,14,18,24,29,162,163,164,165,166,167,161,160,214,204,219,208,45,40,50,55,60,65,70,76,152,157,122,127,132,137,142,147,111,116,80,86,91,96,101,106,30,36,0,6,11,16,20,25,181,182,183,176,177,178,179,180,210,200,215,209 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 = {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 21:46:20 · history