Equation 677 Database

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Magma 7797a2ee3def…

magma 7797a2ee3def
Size
273
Isomorphism class hash
7797a2ee3defa169f220f87a4df4198986f6aaee3b82d2bb7402c196d48386ed
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 23:19:40
Display reorder
117,116,115,112,113,114,85,86,84,110,111,235,266,97,98,96,93,94,95,88,89,87,91,92,90,166,164,165,162,163,161,172,170,171,168,169,167,206,207,205,209,210,208,211,212,244,214,245,213,247,224,246,222,223,221,217,215,216,220,218,219,259,257,258,271,65,63,64,61,62,60,71,69,70,67,68,66,197,198,196,193,194,195,203,204,202,199,200,201,225,226,227,228,229,250,230,231,248,232,233,251,108,109,234,107,105,106,99,100,101,102,103,104,255,263,265,260,13,14,12,16,17,15,19,20,18,22,23,21,0,2,1,4,5,3,7,8,6,10,11,9,145,146,144,141,142,143,237,238,150,147,148,149,189,242,243,190,191,192,187,188,186,183,184,185,261,267,269,272,27,28,29,26,24,25,33,34,35,32,30,31,139,140,138,135,136,137,130,131,129,133,134,132,151,152,153,154,155,249,157,158,156,239,160,159,182,240,241,181,179,180,173,174,175,176,177,178,262,264,268,270,42,43,44,45,46,47,40,41,39,36,37,38,123,121,122,119,120,118,128,126,127,236,125,124,81,82,83,80,78,79,72,73,74,75,76,77,58,59,57,54,55,56,49,50,48,52,53,51,252,253,254,256 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 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 23:19:41 · history