Equation 677 Database

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Magma 314a3f7f7fd7…

magma 314a3f7f7fd7
Size
273
Isomorphism class hash
314a3f7f7fd780b7c2156fbb89f83e6033d596b8f934253d7c0de06cc2afdd42
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 00:47:26
Display reorder
2,1,0,5,3,4,8,6,7,11,9,10,272,60,82,90,61,83,91,62,81,92,63,78,93,64,79,94,65,80,95,66,73,88,67,74,89,68,72,87,69,76,84,70,77,85,71,75,86,107,105,106,103,104,102,98,96,100,101,99,97,271,259,257,263,202,210,172,203,211,173,201,212,171,198,213,168,199,214,169,200,215,170,193,208,178,194,209,179,192,207,177,196,204,174,197,205,175,195,206,176,181,182,180,184,185,183,187,188,189,190,191,186,256,269,270,258,130,138,155,131,139,153,129,140,154,126,141,151,127,142,152,128,143,150,121,136,146,122,137,144,120,135,145,124,132,149,125,133,147,123,134,148,158,156,157,161,159,160,164,162,166,167,165,163,260,261,264,262,109,227,229,110,225,230,108,226,228,112,223,232,113,224,233,111,222,231,115,218,235,116,216,236,114,217,234,118,221,238,119,219,239,117,220,237,243,244,245,242,240,241,249,250,247,248,246,251,268,267,265,266,21,26,45,22,24,46,23,25,47,20,29,44,18,27,42,19,28,43,12,32,36,13,30,37,14,31,38,15,35,39,16,33,40,17,34,41,48,49,50,51,52,53,54,55,59,57,58,56,255,254,252,253 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#bef86252e34aac6c2a18a1e8b323957fca09c4d4a3c476c0116e0c729e633257, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 37, 41, 44, 60} 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 00:47:27 · history