Equation 677 Database

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Magma b4e0e80cd526…

magma b4e0e80cd526
Size
273
Isomorphism class hash
b4e0e80cd526fd9df083b1385ce72087fb78d402b7107c1d3400d4fe1fa01eec
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 20:42:54
Display reorder
72,73,74,75,76,77,78,79,80,81,82,83,254,67,25,16,228,26,17,68,229,66,24,15,230,70,28,12,231,71,29,13,232,69,27,14,233,31,65,22,234,32,63,23,235,30,64,21,236,61,34,18,237,62,35,19,238,60,33,20,239,266,260,259,265,58,199,223,168,200,224,59,169,57,198,222,170,54,202,226,171,55,203,227,172,56,201,225,173,197,49,221,174,195,50,219,175,196,48,220,176,52,193,217,177,53,194,218,178,51,192,216,179,258,264,263,257,186,88,121,204,89,122,187,205,188,87,120,206,189,84,124,207,190,85,125,208,191,86,123,209,94,184,127,210,95,185,128,211,93,183,126,212,180,90,130,213,181,91,131,214,182,92,129,215,261,271,272,262,40,164,109,243,162,110,41,244,39,163,108,245,36,167,112,242,37,165,113,240,38,166,111,241,159,46,115,247,160,47,116,248,161,45,114,249,42,158,118,250,43,156,119,246,44,157,117,251,267,270,269,268,155,133,104,7,134,102,153,8,154,132,103,6,151,136,107,10,152,137,105,11,150,135,106,9,139,146,99,5,140,144,100,3,138,145,101,4,149,142,98,0,147,143,96,2,148,141,97,1,256,255,253,252 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#520f0c8ba72cb86fc7f95b2cd25444b775e13567ed9a2b839438811596de084e, M = {0, 5, 10, 16, 21, 26, 33, 38, 43, 48, 53, 58, 60} 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 20:42:55 · history