Equation 677 Database

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Magma 67e2f7d54445…

magma 67e2f7d54445
Size
273
Isomorphism class hash
67e2f7d54445e6ae0521c2e8cb3f6165106ddeab1ea60ae2311ff7098c22ca17
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
2026-10-08 19:22:20
Display reorder
24,25,26,27,28,29,30,31,32,33,34,35,252,40,58,62,228,59,60,229,41,57,39,61,230,54,36,65,231,55,37,63,232,56,38,64,233,49,46,68,234,50,47,66,235,48,45,67,236,52,42,71,237,53,43,69,238,70,51,44,239,266,260,259,265,91,221,122,171,219,120,172,92,220,90,121,173,217,94,125,170,218,95,123,168,216,93,124,169,227,89,128,177,225,87,126,178,226,88,127,179,223,85,131,176,224,86,129,174,130,222,84,175,258,264,263,257,136,112,96,180,113,97,181,137,111,135,98,182,108,132,99,183,109,133,100,184,110,134,101,185,118,142,102,186,119,143,103,187,117,141,104,188,114,138,105,189,115,139,106,190,107,116,140,191,261,271,272,262,158,73,206,243,74,204,244,156,72,157,205,245,76,161,209,242,77,159,207,240,75,160,208,241,79,164,212,247,80,162,210,248,78,163,211,249,82,167,215,250,83,165,213,246,214,81,166,251,267,270,269,268,20,199,2,150,200,1,151,18,198,19,0,152,202,23,5,153,203,21,3,154,201,22,4,155,197,15,8,148,195,16,6,149,196,17,7,147,193,14,11,144,194,12,9,145,10,192,13,146,256,254,255,253 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#58acf36cbe6044882516075a72a3c87dd19ad7333778c9b60a583a8d5c85fb41, M = {0, 6, 12, 15, 21, 26, 31, 36, 41, 45, 50, 56, 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 2026-10-08 19:22:21 · history