Equation 677 Database

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Magma ce39ba5b6652…

magma ce39ba5b6652
Size
273
Isomorphism class hash
ce39ba5b6652f70157524c6b4e5da59c94971ba936b246c0250bedea7b496f15
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 07:07:57
Display reorder
90,91,92,93,94,95,88,89,87,84,85,86,254,80,105,109,228,106,78,110,229,79,107,108,230,104,83,112,231,81,102,113,232,103,82,111,233,96,75,115,234,97,76,116,235,98,77,114,236,74,99,118,237,72,100,119,238,73,101,117,239,266,260,259,265,71,199,223,168,200,69,224,169,70,198,222,170,202,67,226,171,68,203,227,172,201,66,225,173,197,62,221,174,195,60,219,175,196,61,220,176,65,193,217,177,63,194,218,178,64,192,216,179,258,264,263,257,187,204,48,126,205,188,49,127,186,206,50,128,207,190,51,129,191,208,52,130,209,189,53,131,210,185,54,124,211,183,55,125,212,184,56,123,181,213,57,120,182,214,58,121,180,215,59,122,261,271,272,262,164,33,37,243,34,162,38,244,163,35,36,245,32,167,40,242,165,30,41,240,31,166,39,241,24,159,43,247,25,160,44,248,26,161,42,249,158,27,46,250,156,28,47,246,157,29,45,251,267,270,269,268,9,13,137,155,14,10,135,153,11,12,136,154,16,8,133,151,6,17,134,152,15,7,132,150,19,1,143,146,20,0,141,144,18,2,142,145,3,22,139,149,4,23,140,147,5,21,138,148,256,255,253,252 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#1de75750e9587644a990145f0b96f270fc04381fd8036a009d6bb6ea07359c52, M = {0, 8, 11, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63} 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 07:07:58 · history