Equation 677 Database

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Magma 45fe9288179e…

magma 45fe9288179e
Size
221
Isomorphism class hash
45fe9288179ec554aff7fc184c01df28dfaf6740fc6dd2102455a5ff264c244f
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 21:46:32
Display reorder
195,198,204,185,203,188,186,191,178,205,192,179,184,180,182,189,201,187,177,202,176,196,199,206,200,190,197,183,181,193,194,207,208,209,220,214,212,211,216,210,219,218,215,213,217,166,1,6,23,91,82,5,3,26,96,15,59,148,46,128,36,110,152,164,132,162,161,172,94,83,72,65,105,100,88,80,66,78,43,122,113,155,50,136,38,33,108,53,141,169,55,51,49,138,131,41,37,35,114,29,24,99,18,87,13,79,71,157,64,165,168,170,69,61,62,77,103,101,95,90,85,81,42,127,121,117,30,107,56,52,145,47,135,167,4,10,19,106,67,14,21,7,73,17,8,92,27,60,11,97,75,158,86,160,156,174,119,133,149,111,125,139,153,115,129,143,44,146,109,123,45,151,31,39,142,57,118,163,58,40,54,124,147,34,48,32,137,28,25,74,22,68,20,63,89,171,84,173,159,175,130,154,126,150,120,144,116,140,112,134,9,102,70,98,0,93,2,16,76,12,104 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#12c36c7b075c404ad1fd3f656ab357d26cf582121b46d12c1b704537376fe22b, M = {0} 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 21:46:32 · history