Equation 677 Database

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Magma f4a09c9faa78…

magma f4a09c9faa78
Size
273
Isomorphism class hash
f4a09c9faa78bdb5c18053f4b5408da74eba6dc13176c35ea170a798b43b693f
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 08:04:46
Display reorder
56,54,55,59,57,58,51,52,53,50,48,49,254,21,34,37,228,35,38,22,229,33,23,36,230,30,40,20,231,31,41,18,232,32,39,19,233,25,43,12,234,26,44,13,235,24,42,14,236,28,46,15,237,29,47,16,238,27,45,17,239,266,260,259,265,223,79,199,168,80,200,224,169,78,222,198,170,82,202,226,171,83,203,227,172,81,201,225,173,77,197,221,174,75,195,219,175,76,196,220,176,73,193,217,177,74,194,218,178,72,192,216,179,258,264,263,257,85,186,124,204,187,125,86,205,188,84,123,206,189,120,88,207,190,121,89,208,191,122,87,209,184,130,91,210,185,131,92,211,183,129,90,212,180,126,94,213,181,127,95,214,182,128,93,215,261,271,272,262,11,111,164,243,112,162,9,244,113,10,163,245,110,167,7,242,108,165,8,240,109,166,6,241,117,159,2,247,118,160,1,248,119,161,0,249,116,158,5,250,114,156,3,246,115,157,4,251,267,270,269,268,155,96,69,139,97,70,153,140,98,154,71,138,99,68,151,142,100,66,152,143,101,67,150,141,102,60,146,137,103,61,144,135,104,62,145,136,105,63,149,133,106,64,147,134,107,65,148,132,256,255,253,252 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#0898d182914656a7d8331eed416fb390a2b0882bf44ec0102530c706a89c62d3, M = {0, 6, 12, 16, 21, 26, 31, 36, 41, 46, 51, 56, 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 2026-10-07 08:04:47 · history