Equation 677 Database

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Magma 04a39618b9b4…

magma 04a39618b9b4
Size
273
Isomorphism class hash
04a39618b9b4b59e228984552124ddc8ebdfe746e4102c0cea1a33e9a0e5a7ba
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
2026-10-06 14:03:01
Display reorder
89,87,88,85,86,84,95,93,94,91,92,90,254,63,81,22,228,64,82,23,229,65,83,21,230,62,80,18,231,60,78,19,232,61,79,20,233,69,72,13,234,70,73,14,235,71,74,12,236,68,75,16,237,66,76,17,238,67,77,15,239,266,260,259,265,29,199,223,168,27,200,224,169,28,198,222,170,25,202,226,171,26,203,227,172,24,201,225,173,35,197,221,174,33,195,219,175,34,196,220,176,31,193,217,177,32,194,218,178,30,192,216,179,258,264,263,257,204,186,142,37,205,187,143,38,206,188,141,36,207,189,138,40,208,190,139,41,209,191,140,39,210,184,133,43,211,185,134,44,212,183,132,42,213,180,136,46,214,181,137,47,215,182,135,45,261,271,272,262,8,164,126,243,6,162,127,244,7,163,128,245,11,167,129,242,9,165,130,240,10,166,131,241,3,159,124,247,4,160,125,248,5,161,123,249,2,158,120,250,1,156,121,246,0,157,122,251,267,270,269,268,155,99,117,50,153,100,118,48,154,101,119,49,151,98,116,53,152,96,114,51,150,97,115,52,146,105,108,56,144,106,109,54,145,107,110,55,149,104,111,59,147,102,112,57,148,103,113,58,256,255,253,252 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#05c0aaa7a3560fa146ae1951a40d178d675f2688aa4f7579703e2b967da3180b, M = {0, 5, 10, 15, 21, 25, 30, 35, 40, 46, 51, 56, 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 2026-10-06 14:03:03 · history