Equation 677 Database

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Magma d7004471fcfd…

magma d7004471fcfd
Size
273
Isomorphism class hash
d7004471fcfd5bfb32cd407b398af0939e26b080a714752addece4352ef93354
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
2026-10-09 02:30:59
Display reorder
83,81,82,79,80,78,74,72,73,77,75,76,254,60,59,11,228,61,57,9,229,62,58,10,230,63,7,231,55,56,64,8,232,65,54,6,233,66,50,2,234,67,48,1,235,68,49,0,236,69,53,5,237,51,70,3,238,52,71,4,239,266,260,259,265,199,42,223,168,200,43,224,169,198,44,222,170,202,226,171,45,46,203,227,172,201,47,225,173,197,40,221,174,195,41,219,175,196,39,220,176,193,36,217,177,37,194,218,178,38,192,216,179,258,264,263,257,186,204,121,112,187,205,122,113,188,206,120,111,189,124,108,207,208,190,125,109,191,209,123,110,184,210,127,118,185,211,128,119,183,212,126,117,180,213,130,114,214,181,131,115,215,182,129,116,261,271,272,262,99,21,164,243,100,22,162,244,101,23,163,245,98,167,242,20,18,96,165,240,97,19,166,241,105,12,159,247,106,13,160,248,107,14,161,249,104,15,158,250,16,102,156,246,17,103,157,251,267,270,269,268,84,133,153,34,85,134,154,35,86,132,155,33,87,152,30,136,137,88,150,31,89,135,151,32,90,139,144,25,91,140,145,26,92,138,146,24,93,142,147,28,143,94,148,29,141,95,149,27,256,255,253,252 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#dc2fe3473be348561d898626a2f45bbebd7964bafd5487f2fff34f8adc67b3cf, M = {0, 5, 10, 15, 20, 27, 33, 38, 43, 48, 53, 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 2026-10-09 02:31:00 · history