Equation 677 Database

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Magma 663a450bc19c…

magma 663a450bc19c
Size
273
Isomorphism class hash
663a450bc19c889931bbcc344ef27034da3fb0528d94912da76c8b663e93919c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 272) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 03:16:36
Display reorder
67,68,66,70,71,69,65,63,64,61,62,60,254,35,52,37,228,33,38,53,229,34,36,51,230,31,40,48,231,32,41,49,232,30,39,50,233,58,43,26,234,59,44,24,235,57,42,25,236,54,46,29,237,55,47,27,238,56,45,28,239,266,260,259,265,95,223,199,132,93,200,224,133,94,198,222,134,91,202,226,135,92,203,227,136,90,201,225,137,221,197,86,138,219,195,84,139,220,196,85,140,217,193,89,141,218,194,87,142,216,192,88,143,258,264,263,257,186,107,152,204,187,150,105,205,188,151,106,206,189,155,103,207,190,153,104,208,191,154,102,209,98,147,184,210,96,148,185,211,97,149,183,212,101,146,180,213,99,144,181,214,100,145,182,215,261,271,272,262,177,22,128,243,178,126,23,244,179,127,21,245,176,131,18,242,174,129,19,240,175,130,20,241,13,123,168,247,14,124,169,248,12,125,170,249,16,122,171,250,17,120,172,246,15,121,173,251,267,270,269,268,119,75,0,160,117,2,76,161,118,1,77,159,115,4,74,156,116,5,72,157,114,3,73,158,81,7,110,166,82,8,108,167,83,6,109,165,80,10,113,162,78,11,111,163,79,9,112,164,256,255,253,252 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 273 = 13 + 5*52, 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#c8b00e8ba82c54826bf93ef2b9b2d8eeb61b8eb7ac0797b661231f1bb38e050b, M = {0, 7, 12, 17, 22, 27, 31, 36, 41, 45, 50, 55, 62} 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, 52): MacNeish's product over GF(4) x GF(13); 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 2026-10-07 03:16:37 · history