Equation 677 Database

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Magma 3a3259b4570c…

magma 3a3259b4570c
Size
273
Isomorphism class hash
3a3259b4570c17388b56e17b0cfafb7aafa0e341c59657a1b837683112ce82f6
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 03:54:27
Display reorder
125,123,124,121,122,120,131,129,130,127,128,126,253,133,147,17,228,148,15,229,134,149,132,16,230,136,146,13,231,137,144,14,232,135,145,12,233,153,139,23,234,21,154,140,235,155,138,22,236,152,142,19,237,150,143,20,238,151,141,18,239,266,260,259,265,53,221,211,60,219,212,61,51,220,52,210,62,49,217,214,63,50,218,215,64,48,216,213,65,227,59,209,66,207,225,57,67,226,58,208,68,223,55,205,69,224,56,206,70,222,54,204,71,258,264,263,257,101,80,172,84,78,173,85,99,79,100,171,86,97,83,168,87,98,81,169,88,96,82,170,89,75,107,178,90,179,76,105,91,77,106,177,92,74,103,174,93,72,104,175,94,73,102,176,95,261,271,272,262,4,193,158,243,194,156,244,5,192,3,157,245,1,196,161,242,0,197,159,240,2,195,160,241,199,10,164,247,162,200,11,248,198,9,163,249,202,6,167,250,203,7,165,246,201,8,166,251,267,270,269,268,186,112,32,38,113,30,36,187,111,188,31,37,189,108,35,41,190,109,33,39,191,110,34,40,118,184,27,44,28,119,185,42,117,183,29,43,114,180,26,47,115,181,24,45,116,182,25,46,256,254,255,252 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#be22598f61f867b223264cf52ecf408910eea148415a700aef96392fba43b30a, M = {0, 6, 12, 17, 22, 27, 31, 37, 41, 45, 50, 55, 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 2026-10-07 03:54:29 · history