Equation 677 Database

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Magma 364125fb24af…

magma 364125fb24af
Size
221
Isomorphism class hash
364125fb24af10ee74f7ded71798b48aa86888ba368d7cd0ae150ff3906fcc10
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 22:02:52
Display reorder
220,196,63,37,53,190,56,38,54,57,191,39,55,177,58,32,48,178,59,33,49,50,60,179,34,61,51,180,35,52,62,181,36,46,47,40,42,43,44,45,41,213,208,206,217,174,20,14,30,175,21,15,31,22,176,8,24,189,23,9,25,188,16,10,26,27,17,171,11,18,28,172,12,29,19,173,13,3,4,5,7,1,0,2,6,209,219,214,205,194,115,109,125,187,116,110,126,117,195,111,127,170,118,104,120,166,119,105,121,122,112,167,106,113,123,168,107,124,114,169,108,98,99,100,102,103,96,97,101,216,204,210,212,163,68,84,78,164,69,85,79,70,161,86,72,192,71,87,73,193,64,80,74,75,65,165,81,66,76,160,82,77,67,162,83,93,94,95,89,90,91,92,88,207,215,218,211,199,131,147,141,197,132,148,142,133,198,149,143,182,134,150,136,183,135,151,137,138,128,184,144,129,139,185,145,140,130,186,146,156,157,158,152,153,154,155,159,203,201,200,202 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#3cd0748015bf78420965b6c1c7cbca61850caba7fcf08520f32ef27e9761bd24, M = {40} 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 22:02:53 · history