Equation 677 Database

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Magma 0db0f72bf95a…

magma 0db0f72bf95a
Size
273
Isomorphism class hash
0db0f72bf95ac63658553a8f925e5abbc45a8f8584910a4368a4dbe0287bc27e
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 02:05:04
Display reorder
113,111,112,109,110,108,119,117,118,115,116,114,254,107,88,122,228,89,120,229,105,106,87,121,230,84,103,125,231,85,104,123,232,86,102,124,233,94,98,128,234,126,95,96,235,93,97,127,236,90,101,131,237,91,99,129,238,92,100,130,239,266,260,259,265,191,221,19,150,219,20,151,189,190,220,18,152,217,187,22,153,218,188,23,154,216,186,21,155,227,182,17,148,15,225,180,149,226,181,16,147,223,185,13,144,224,183,14,145,222,184,12,146,258,264,263,257,24,36,156,168,37,157,169,25,26,38,158,170,39,27,159,171,40,28,160,172,41,29,161,173,42,30,162,174,163,43,31,175,44,32,164,176,45,33,165,177,46,34,166,178,47,35,167,179,261,271,272,262,133,0,206,243,2,204,244,134,132,1,205,245,4,136,209,242,5,137,207,240,3,135,208,241,7,139,212,247,210,8,140,248,6,138,211,249,10,142,215,250,11,143,213,246,9,141,214,251,267,270,269,268,48,199,60,74,200,61,72,49,50,198,62,73,202,51,63,77,203,52,64,75,201,53,65,76,197,54,66,80,67,195,55,78,196,56,68,79,193,57,69,83,194,58,70,81,192,59,71,82,256,252,255,253 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#dd5d8cb242321da00ce62fc2d476849be658b6b0a3d2fd229095425016dc303c, M = {0, 5, 10, 15, 20, 25, 31, 37, 41, 45, 50, 55, 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 02:05:05 · history