Equation 677 Database

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Magma 12bc5a065a97…

magma 12bc5a065a97
Size
273
Isomorphism class hash
12bc5a065a97fc345435de64905ca274898885c5ee49650e511d2b07c03d672e
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 09:59:06
Display reorder
43,44,42,46,47,45,41,39,40,37,38,36,254,72,17,66,228,73,15,67,229,74,16,68,230,13,75,69,231,14,76,70,232,77,71,233,12,23,78,64,234,21,79,65,235,22,80,63,236,81,19,60,237,82,20,61,238,83,18,62,239,266,260,259,265,199,102,223,148,200,103,224,149,198,104,222,147,105,202,226,144,106,203,227,145,201,225,146,107,100,197,221,154,101,195,219,155,99,196,220,153,193,96,217,150,194,97,218,151,192,98,216,152,258,264,263,257,160,91,109,204,161,92,110,205,159,90,108,206,94,156,112,207,95,157,113,208,158,111,209,93,89,166,115,210,87,167,116,211,88,165,114,212,162,85,118,213,163,86,119,214,164,84,117,215,261,271,272,262,135,180,8,243,136,181,6,244,137,182,7,245,183,134,11,242,184,132,9,240,133,10,241,185,186,141,3,247,187,142,4,248,188,143,5,249,140,189,2,250,138,190,1,246,139,191,0,251,267,270,269,268,29,120,59,176,27,121,57,174,28,122,58,175,123,25,55,179,124,26,56,177,24,54,178,125,126,35,50,171,127,33,48,172,128,34,49,173,31,129,53,170,32,130,51,168,30,131,52,169,256,255,253,252 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#15e0002a5ecb0f8e7ea13fca6591bd645ffece494b3bd71abe8f3bbcdb21ed68, M = {0, 5, 10, 15, 21, 26, 33, 38, 43, 48, 53, 58, 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 09:59:07 · history