Equation 677 Database

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Magma a3f394df5432…

magma a3f394df5432
Size
321
Isomorphism class hash
a3f394df543211dbc2eea17beb936b25fc874bd2574eae6e7cbab143f9266b69
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:37:09
Display reorder
300,88,158,196,178,180,181,156,89,197,179,157,182,87,195,177,183,84,161,192,174,85,184,159,193,175,185,86,160,194,176,164,94,186,202,169,95,187,203,162,170,93,188,201,163,168,189,90,198,167,172,190,91,199,165,173,191,92,200,166,171,315,316,301,303,56,268,271,270,269,273,272,54,275,274,264,265,55,267,266,252,59,253,255,254,57,256,257,259,258,260,58,261,263,262,293,51,292,294,295,52,296,298,297,299,53,288,291,289,290,276,50,278,277,279,280,48,282,281,283,285,49,286,284,287,320,319,318,317,105,236,2,71,237,239,238,106,1,69,234,235,107,0,70,228,104,229,5,67,102,231,230,3,68,233,103,232,4,66,249,96,248,8,62,97,250,6,251,60,98,246,7,247,61,240,99,11,241,65,242,100,9,243,63,244,101,10,245,64,310,309,307,308,21,38,112,220,126,127,36,22,113,221,37,128,23,111,219,129,20,41,108,216,18,130,39,109,217,131,19,40,110,218,44,12,124,118,226,13,125,119,42,227,14,123,117,43,225,120,15,114,47,222,121,16,115,45,223,122,17,116,46,224,311,312,306,302,26,72,145,208,143,141,73,24,146,209,74,142,25,144,207,139,29,75,148,204,27,140,76,149,205,138,28,77,147,206,78,32,134,151,214,30,132,152,79,215,31,133,150,80,213,137,35,154,81,210,135,33,155,82,211,136,34,153,83,212,314,313,304,305 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#6997491de262e367994a4a50c6f8055cb54c2a6a0260cea123f554e749c551e0, M = {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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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 2026-10-01 22:37:10 · history