Equation 677 Database

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Magma 6857fd8e62df…

magma 6857fd8e62df
Size
221
Isomorphism class hash
6857fd8e62dfa8e77514cb14a14d66575bc81d0a751c46a955c7bc92832afc03
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 22:03:08
Display reorder
220,157,152,122,127,132,137,142,147,185,71,26,115,186,76,31,81,40,187,36,86,46,188,1,91,51,189,6,96,56,190,10,101,61,191,106,19,184,66,111,20,202,217,212,206,156,151,120,125,131,136,141,146,181,70,25,117,182,75,30,82,41,183,35,87,45,176,0,92,50,177,7,97,55,178,12,102,60,179,107,15,180,65,112,21,200,219,210,207,158,153,123,128,133,138,143,148,170,73,27,116,171,78,32,80,43,172,37,85,48,173,2,90,53,174,5,95,58,175,11,100,63,168,105,16,169,68,110,22,203,215,211,205,159,154,124,129,134,139,144,149,163,74,29,119,164,79,34,84,44,165,39,89,49,166,4,94,54,167,9,99,59,161,14,104,64,160,109,18,162,69,114,24,204,218,214,209,155,150,121,126,130,135,140,145,193,72,28,118,194,77,33,83,42,195,38,88,47,196,3,93,52,197,8,98,57,198,13,103,62,199,108,17,192,67,113,23,201,216,213,208 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#9ac61f33e0de3061260327cd1f8ec493e58b27cc56b59ca78e22c7e08c8ddabf, 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 22:03:09 · history