Equation 677 Database

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Magma b9a659ad7820…

magma b9a659ad7820
Size
621
Isomorphism class hash
b9a659ad7820535d0cb5b23da9bde004c2a60a45325bd1c5487ec60b10fa262c
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 466 (nullity 155) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 13:24:09
Display reorder
500,182,287,226,433,299,184,265,234,313,273,244,193,63,19,12,482,221,188,293,231,260,256,251,268,36,14,57,442,307,281,215,238,200,275,248,196,279,207,304,284,216,186,296,227,46,31,42,447,38,79,59,440,1,69,21,438,291,222,258,303,82,51,102,468,354,415,364,428,134,87,142,456,396,345,409,358,419,368,432,375,323,386,335,400,108,163,119,472,128,83,140,454,147,152,106,469,118,171,126,495,378,326,389,338,155,110,164,461,174,131,86,479,330,394,341,405,112,168,123,474,136,91,145,458,395,317,357,392,431,353,385,427,348,383,423,344,179,169,101,478,414,334,373,411,332,371,408,328,124,157,92,462,399,320,361,243,206,211,214,220,225,230,183,250,312,203,192,306,11,2,6,481,45,48,53,449,56,62,67,493,286,292,298,255,33,35,5,446,263,266,271,274,58,65,68,452,290,295,302,232,237,241,247,205,209,213,219,224,28,81,41,439,78,9,0,476,8,100,135,470,97,130,160,455,370,404,325,365,154,90,121,467,85,117,148,492,356,388,430,350,144,173,105,488,170,104,138,471,217,228,253,308,180,191,259,267,276,280,285,297,32,39,16,443,223,314,201,197,187,185,264,272,60,70,73,485,239,249,208,331,406,366,321,397,359,315,390,351,425,381,342,417,137,98,161,463,94,156,122,453,149,113,176,489,347,422,379,339,165,132,54,451,434,294,257,240,17,23,27,437,310,194,199,189,261,269,277,282,288,300,235,245,20,25,30,445,15,77,3,490,49,146,109,473,141,103,167,464,333,410,369,324,153,120,84,465,111,175,143,460,420,376,336,412,129,95,158,486,88,150,115,483,547,612,499,514,607,582,581,583,604,568,566,567,590,555,554,556,600,541,526,532,618,519,517,503,609,537,512,545,613,501,515,498,591,558,557,559,610,565,563,564,611,561,560,562,596,522,508,509,595,548,549,550,606,580,578,579,598,530,524,496,594,553,552,551,603,504,511,520,615,544,528,535,605,570,569,571,617,502,516,518,592,587,588,589,597,507,506,523,599,497,525,531,616,574,573,572,593,586,585,584,619,575,576,577,620,538,539,540,602,521,510,505,608,546,513,536,601,533,527,542,614,534,529,543,413,337,377,421,346,384,429,355,393,318,362,401,93,125,159,457,374,416,340,380,424,349,387,435,116,151,89,477,403,329,372,210,246,236,301,289,283,278,270,262,190,198,195,311,4,26,22,441,37,43,75,491,64,55,50,494,181,305,202,252,29,24,114,466,319,363,402,327,127,162,99,487,418,343,382,426,352,391,316,360,398,322,367,407,96,133,166,459,139,172,107,480,177,47,178,484,10,13,80,444,212,204,242,233,76,72,66,450,52,44,7,436,309,254,229,218,18,40,34,475,74,71,61,448 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 621 = 1 + 5*124, 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 = P(31, 15, magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5, 0), M = {4} 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, 124): MacNeish's product over GF(4) x GF(31); 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. P(l, q, S, v) is the Paley pencil over Z/l with multiplier q on the seed S of order K + 1 with vertex v: S is relabelled with v as 0 and its other elements as 1..K in increasing order; the points are 0 (the vertex) and 1 + K x + t for (x, t) in Z/l x Z/K; points of one line, or a point and the vertex, multiply as in S (0 the vertex, t + 1 the point (x, t)); and (x, s)*(y, t) for x != y is ((1-q)x + qy, t) when y - x is a nonzero square mod l, else ((1-q)x + qy, -s-t mod K). Equation 255: satisfied. Idempotent elements: 621.

last edited by qawbecrdtey at 2026-10-06 13:24:10 · history