Equation 677 Database

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Magma f1222b5008e8…

magma f1222b5008e8
Size
273
Isomorphism class hash
f1222b5008e8752810b634fef55927bf83d7b9aeaa16a0f86e2b6c8b40d1d59a
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
2026-10-08 09:38:14
Display reorder
5,3,4,0,2,1,11,9,10,7,8,6,272,220,219,221,218,216,217,225,226,227,224,222,223,114,115,116,117,118,119,112,113,111,108,109,110,128,126,127,131,129,130,123,124,125,122,120,121,168,169,170,171,172,173,174,175,176,177,178,179,262,257,259,268,84,86,85,89,87,88,92,90,91,95,93,94,166,167,165,162,163,164,157,158,156,160,161,159,100,101,99,96,97,98,106,107,105,102,103,104,210,211,212,213,214,215,208,209,207,204,205,206,256,264,269,258,240,242,241,245,243,244,248,246,247,251,249,250,195,196,197,194,192,193,201,202,203,200,198,199,78,79,80,81,82,83,76,77,75,72,73,74,152,150,151,155,153,154,147,148,149,146,144,145,260,265,271,263,142,141,143,140,138,139,132,133,134,135,136,137,62,60,61,65,63,64,68,66,67,71,69,70,182,180,181,185,183,184,188,186,187,191,189,190,230,228,229,233,231,232,236,234,235,239,237,238,261,266,270,267,42,44,43,47,45,46,39,40,41,38,36,37,18,19,20,21,22,23,16,17,15,12,13,14,32,30,31,35,33,34,27,28,29,26,24,25,51,52,53,50,48,49,57,58,59,56,54,55,252,253,254,255 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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 2026-10-08 09:38:15 · history