Equation 677 Database

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Magma a814a14db3bc…

magma a814a14db3bc
Size
221
Isomorphism class hash
a814a14db3bc2e2c6906a9f451a2a4b6ac3983dd856aaa842256f1d2667ab9b1
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 166 (nullity 55) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:14:56
Display reorder
220,99,128,112,38,42,205,83,169,164,109,72,175,106,92,84,13,201,15,137,0,189,51,27,179,8,97,193,56,24,140,33,2,86,93,102,29,188,165,150,122,5,96,59,117,141,146,119,46,32,200,85,182,168,105,82,178,116,121,87,58,204,18,142,41,191,6,21,174,23,107,195,55,17,132,19,26,73,136,144,50,192,167,148,103,48,139,44,120,101,138,133,4,28,207,79,166,177,149,78,170,129,94,80,11,194,7,100,36,198,9,54,181,43,124,190,31,34,127,1,22,81,113,143,39,203,172,131,110,47,135,16,104,155,158,215,61,65,210,90,216,184,218,89,187,162,161,91,212,211,60,153,71,209,67,217,186,70,160,219,64,213,157,69,68,88,214,154,66,208,185,156,159,62,163,63,152,130,125,123,25,14,206,75,173,171,151,74,183,118,134,76,10,196,45,126,3,202,12,57,180,52,108,199,53,20,115,35,40,77,111,145,37,197,176,147,114,49,98,30,95 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#f2ff036103ce87dd22beb1b750344314c69ce6fbd5e0a995701630860538525a, M = {1} 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: 221.

last edited by qawbecrdtey at 2026-10-01 22:14:58 · history