Equation 677 Database

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Magma a001fb6522a1…

magma a001fb6522a1
Size
273
Isomorphism class hash
a001fb6522a1ffd416b5c129bbd22a424169afa54fded7443e1b19ca4bf5e0df
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 03:22:17
Display reorder
44,42,43,47,45,46,39,40,41,38,36,37,254,26,18,228,110,24,108,19,229,109,25,20,230,29,113,21,231,27,111,22,232,28,112,23,233,116,32,16,234,114,30,17,235,115,31,15,236,35,119,12,237,33,117,13,238,34,118,14,239,266,260,259,265,96,199,148,223,97,224,200,149,222,98,198,147,99,226,202,144,100,227,203,145,101,225,201,146,221,102,197,154,219,103,195,155,220,104,196,153,105,217,193,150,106,218,194,151,107,216,192,152,258,264,263,257,71,49,204,160,69,161,50,205,159,70,48,206,67,156,52,207,68,157,53,208,66,158,51,209,166,62,55,210,167,60,56,211,165,61,54,212,65,162,58,213,63,163,59,214,64,164,57,215,261,271,272,262,181,134,243,91,182,92,132,244,90,180,133,245,184,94,137,242,185,95,135,240,183,93,136,241,89,187,140,247,87,188,138,248,88,186,139,249,190,85,143,250,191,86,141,246,189,84,142,251,267,270,269,268,83,126,11,175,81,176,127,9,174,82,128,10,79,178,129,7,80,179,130,8,78,177,131,6,173,74,124,2,171,72,125,1,172,73,123,0,77,169,120,5,75,170,121,3,76,168,122,4,256,252,253,255 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#41328e14760452489c50b79fcc49c074869181cbfbd0a816da081f28123ef346, M = {0, 5, 12, 15, 20, 25, 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 2026-10-09 03:22:23 · history