Equation 677 Database

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Magma ae868a9dab3a…

magma ae868a9dab3a
Size
273
Isomorphism class hash
ae868a9dab3aadd89ef1f927e368e0a7b7bc26f01ecc1f37222e05b4ffde148f
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 00:16:25
Display reorder
96,97,98,99,100,101,102,103,104,105,106,107,254,90,47,228,49,50,91,45,229,48,92,46,230,52,93,43,231,53,94,44,232,51,95,42,233,88,55,38,234,89,56,36,235,87,54,37,236,84,58,41,237,85,59,39,238,86,57,40,239,266,260,259,265,223,199,149,83,81,224,200,147,82,222,198,148,79,226,202,145,80,227,203,146,78,225,201,144,221,74,197,155,219,72,195,153,220,73,196,154,217,77,193,151,218,75,194,152,216,76,192,150,258,264,263,257,204,159,111,31,32,205,160,112,30,206,161,113,34,207,158,110,35,208,156,108,33,209,157,109,210,29,165,117,211,27,166,118,212,28,167,119,213,25,164,116,214,26,162,114,215,24,163,115,261,271,272,262,181,134,243,64,65,182,132,244,63,180,133,245,60,184,137,242,61,185,135,240,62,183,136,241,187,70,140,247,188,71,138,248,186,69,139,249,190,66,143,250,191,67,141,246,189,68,142,251,267,270,269,268,175,126,5,23,21,176,127,3,22,174,128,4,19,178,129,0,20,179,130,2,18,177,131,1,173,14,124,11,171,12,125,9,172,13,123,10,169,17,120,7,170,15,121,8,168,16,122,6,256,252,253,255 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#07e8f68f5124a8e3a0938e8678de1c72ed7349b338061e203d5db711c48e18fa, M = {0, 5, 10, 17, 20, 27, 31, 36, 41, 45, 50, 55, 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 00:16:26 · history