Equation 677 Database

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Magma 512ec6b514b5…

magma 512ec6b514b5
Size
273
Isomorphism class hash
512ec6b514b5a46d5de53e7be87c1a1f3fa3ec29e4ee76fccd6249b4985c89b1
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 03:27:49
Display reorder
59,57,58,55,56,54,50,48,49,53,51,52,254,75,44,65,228,63,76,42,229,77,64,43,230,61,74,47,231,62,72,45,232,60,73,46,233,81,71,39,234,82,69,40,235,83,70,41,236,80,67,38,237,78,68,36,238,79,66,37,239,266,260,259,265,199,223,149,101,147,200,224,99,198,148,222,100,145,202,226,97,146,203,227,98,144,201,225,96,197,155,221,107,195,153,219,105,196,154,220,106,193,151,217,103,194,152,218,104,192,150,216,102,258,264,263,257,156,111,24,204,25,157,112,205,158,26,113,206,27,159,110,207,28,160,108,208,29,161,109,209,162,30,117,210,163,31,118,211,164,32,119,212,165,33,116,213,166,34,114,214,167,35,115,215,261,271,272,262,86,134,180,243,181,84,132,244,85,182,133,245,183,89,137,242,184,87,135,240,185,88,136,241,92,186,140,247,90,187,138,248,91,188,139,249,95,189,143,250,93,190,141,246,94,191,142,251,267,270,269,268,128,2,173,14,171,126,1,12,127,172,0,13,169,131,5,17,170,129,3,15,168,130,4,16,123,179,8,20,124,177,6,18,125,178,7,19,122,175,11,23,120,176,9,21,121,174,10,22,256,255,253,252 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#f3708acaf97ab90d0e627f94c9229dfefc0b06412aed9a05696d0ed9b4a78cdc, M = {0, 7, 12, 15, 20, 25, 31, 36, 41, 46, 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 2026-10-08 03:27:51 · history