Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 2b6fec1199aa…

magma 2b6fec1199aa
Size
381
Isomorphism class hash
2b6fec1199aab6678e46a8474645f1be7178632d5f969093efc6c63e46c4d3eb
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:20:23
Display reorder
380,18,69,168,297,110,19,70,111,169,298,71,20,112,170,299,66,21,113,171,295,22,67,108,172,294,109,68,23,173,296,308,99,148,243,221,100,309,149,244,216,101,325,147,245,217,306,96,146,240,218,326,97,145,241,219,307,98,144,242,220,256,252,253,254,255,257,343,356,360,348,367,331,337,368,344,357,92,33,236,260,128,93,34,129,237,261,35,94,130,238,262,30,95,131,239,263,90,31,126,234,258,127,32,91,235,259,312,76,114,224,181,77,313,119,225,182,72,328,117,226,183,310,73,118,227,184,327,74,115,222,185,311,75,116,223,180,274,270,271,272,273,275,332,371,369,353,358,336,346,362,338,372,134,13,278,160,54,135,14,55,281,161,15,136,56,279,156,16,137,57,276,157,133,17,58,277,158,59,12,132,280,159,323,78,8,282,167,79,319,9,287,162,80,320,10,286,163,321,81,11,285,164,329,82,6,283,165,318,83,7,284,166,206,208,209,204,205,207,340,363,359,351,364,330,333,361,350,355,65,140,213,186,102,60,141,103,214,187,142,61,104,215,188,143,62,105,210,189,63,139,106,211,190,107,138,64,212,191,316,28,36,178,290,29,317,37,179,293,24,314,38,174,291,315,25,39,175,289,324,26,40,176,292,322,27,41,177,288,248,250,251,246,247,249,352,370,373,349,366,334,341,365,342,374,1,47,151,233,120,0,42,121,150,228,43,2,122,152,229,44,3,123,153,230,4,45,125,154,231,124,46,5,155,232,305,51,89,199,195,52,300,84,200,196,53,301,85,201,197,302,48,86,202,192,303,49,87,203,193,304,50,88,198,194,264,266,267,268,269,265,347,379,377,354,376,335,339,378,345,375 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#2945041d3247ddd899a6b4f5b12124f9357fdf3bcea91b9501960cadbcfe7b88, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:20:24 · history