Equation 677 Database

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Magma 5974a151e2f0…

magma 5974a151e2f0
Size
273
Isomorphism class hash
5974a151e2f05dcbba55241b436939940baa7dd7a788dbf6ebebf4ac494b75af
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 20:09:09
Display reorder
37,38,36,40,41,39,43,44,42,46,47,45,253,8,25,23,228,26,21,229,6,7,24,22,230,11,28,19,231,9,29,20,232,10,27,18,233,31,3,14,234,4,12,32,235,5,13,30,236,2,17,34,237,1,15,35,238,0,16,33,239,266,260,259,265,70,221,211,180,219,212,181,71,69,220,210,182,66,217,214,183,67,218,215,184,68,216,213,185,227,61,209,186,62,207,225,187,60,208,226,188,64,205,223,189,65,206,224,190,63,204,222,191,258,264,263,257,198,83,154,118,81,155,119,199,200,82,153,117,201,79,150,114,202,80,151,115,203,78,152,116,74,196,145,109,197,146,72,110,195,144,73,108,192,148,77,112,193,149,75,113,194,147,76,111,261,271,272,262,103,176,138,243,174,139,244,104,102,175,140,245,106,179,141,242,107,177,142,240,105,178,143,241,171,101,136,247,99,137,172,248,100,135,173,249,97,132,170,250,98,133,168,246,96,134,169,251,267,270,269,268,131,49,165,95,50,166,93,129,130,48,167,94,127,52,164,91,128,53,162,92,126,51,163,90,55,122,156,86,120,157,56,84,121,158,54,85,125,159,58,89,123,160,59,87,124,161,57,88,256,254,255,252 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#164604ba66664ae7e7b126fe65d39300d84fb27e5ce614035873663e987c6567, M = {0, 5, 10, 16, 21, 26, 31, 35, 40, 46, 51, 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 2026-10-06 20:09:10 · history