Equation 677 Database

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Magma 0743976acd93…

magma 0743976acd93
Size
273
Isomorphism class hash
0743976acd93ae5b0855a6bbf85ecaf4f9d4caae3716799eeeedc71ce51137be
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
2026-10-06 10:11:55
Display reorder
67,68,66,70,71,69,65,63,64,61,62,60,254,73,20,228,55,74,56,18,229,72,54,19,230,76,58,23,231,77,59,21,232,75,57,22,233,79,53,15,234,80,51,16,235,78,52,17,236,49,82,14,237,50,83,12,238,48,81,13,239,266,260,259,265,100,199,149,223,101,224,200,147,99,222,198,148,96,226,202,145,97,227,203,146,98,225,201,144,106,221,197,155,107,219,195,153,105,220,196,154,217,102,193,151,218,103,194,152,216,104,192,150,258,264,263,257,1,159,111,204,0,205,160,112,2,206,161,113,3,207,158,110,4,208,156,108,5,209,157,109,6,210,165,117,7,211,166,118,8,212,167,119,213,9,164,116,214,10,162,114,215,11,163,115,261,271,272,262,88,134,243,181,89,182,132,244,87,180,133,245,84,184,137,242,85,185,135,240,86,183,136,241,94,187,140,247,95,188,138,248,93,186,139,249,190,90,143,250,191,91,141,246,189,92,142,251,267,270,269,268,42,126,44,175,45,176,127,46,47,174,128,43,41,178,129,37,36,179,130,38,39,177,131,40,25,173,124,26,27,171,125,28,29,172,123,24,169,30,120,33,170,32,121,34,168,35,122,31,256,252,253,255 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#33fc7ab4b4817466950310b35dd4cd44cb4b00aed5b55945bbae0672c2180aa2, M = {0, 5, 10, 15, 20, 25, 30, 38, 43, 48, 53, 58, 61} 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 2026-10-06 10:11:58 · history