Equation 677 Database

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Magma 8940e2e672fe…

magma 8940e2e672fe
Size
273
Isomorphism class hash
8940e2e672feae4045f4f8254e87a1ff65f69cb21f2f5c90ab08d99ca4636320
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 14:18:13
Display reorder
74,72,73,77,75,76,80,78,79,83,81,82,254,56,69,0,228,70,54,2,229,55,71,1,230,68,59,4,231,66,57,5,232,67,58,3,233,51,7,60,234,52,8,61,235,53,6,62,236,50,10,63,237,48,11,64,238,65,49,9,239,266,260,259,265,199,47,223,168,45,200,224,169,198,46,222,170,43,202,226,171,44,203,227,172,42,201,225,173,197,221,38,174,195,219,36,175,196,220,37,176,193,217,41,177,194,218,39,178,40,192,216,179,258,264,263,257,143,186,33,204,187,141,34,205,142,188,35,206,189,139,32,207,190,140,30,208,191,138,31,209,134,24,184,210,132,25,185,211,133,26,183,212,137,27,180,213,135,28,181,214,182,136,29,215,261,271,272,262,164,16,125,243,17,162,123,244,163,15,124,245,12,167,121,242,13,165,122,240,14,166,120,241,159,131,22,247,160,129,23,248,161,130,21,249,158,127,18,250,156,128,19,246,20,157,126,251,267,270,269,268,155,98,86,109,96,153,84,110,154,97,85,108,101,151,89,112,99,152,87,113,100,150,88,111,146,92,104,115,144,90,102,116,145,91,103,114,149,95,107,118,147,93,105,119,106,148,94,117,256,255,253,252 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#65ec2d14586b016399098bfd783683584e63e97f4655962a7b7e32e1fef46a76, M = {0, 9, 11, 15, 21, 26, 31, 36, 41, 45, 50, 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 2026-10-07 14:18:15 · history