Equation 677 Database

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Magma 45abfcded387…

magma 45abfcded387
Size
273
Isomorphism class hash
45abfcded387b0f8bdaee68dfb21b83358ec6ec22c2fa212a5db3101c6354c83
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 22:33:02
Display reorder
92,90,91,95,93,94,87,88,89,86,84,85,254,67,76,12,228,68,77,13,229,66,14,75,230,70,72,15,231,71,73,16,232,69,74,17,233,65,82,18,234,63,83,19,235,64,81,20,236,61,78,21,237,62,79,22,238,60,80,23,239,266,260,259,265,59,199,223,168,57,200,224,169,58,222,198,170,55,202,226,171,56,203,227,172,54,201,225,173,50,197,221,174,48,195,219,175,49,196,220,176,53,193,217,177,51,194,218,178,52,192,216,179,258,264,263,257,186,36,142,204,187,37,143,205,188,141,38,206,189,39,138,207,190,40,139,208,191,41,140,209,184,42,133,210,185,43,134,211,183,44,132,212,180,45,136,213,181,46,137,214,182,47,135,215,261,271,272,262,6,164,126,243,7,162,127,244,8,128,163,245,9,167,129,242,10,165,130,240,11,166,131,241,4,159,124,247,5,160,125,248,3,161,123,249,1,158,120,250,0,156,121,246,2,157,122,251,267,270,269,268,155,117,96,24,153,118,97,25,154,98,119,26,151,116,99,27,152,114,100,28,150,115,101,29,146,108,102,30,144,109,103,31,145,110,104,32,149,111,105,33,147,112,106,34,148,113,107,35,256,255,253,252 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#c93f531644bb5fd38eabd6a6f62492ff6d9a38e5937df79a955f96fa67b29b12, M = {0, 6, 10, 16, 21, 26, 30, 35, 40, 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 2026-10-08 22:33:03 · history