Equation 677 Database

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Magma 87230fcd164f…

magma 87230fcd164f
Size
707
Isomorphism class hash
87230fcd164ffa9e6686dadb303375d0b2a73fa836dd55a0e9677c3e4d6159e2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 16:32:30
Display reorder
603,604,605,601,600,602,706,173,155,190,567,158,586,355,590,596,578,558,178,185,166,337,409,575,550,554,168,150,191,555,568,159,587,356,591,597,579,560,179,180,167,338,410,570,546,169,151,186,556,569,160,582,357,592,598,580,561,174,181,162,339,411,571,547,170,152,187,557,564,161,583,358,593,599,581,562,175,182,163,340,412,572,548,171,153,188,553,565,156,584,359,588,594,576,563,176,183,164,341,413,573,549,552,172,154,189,566,157,585,354,589,595,577,559,177,184,165,336,408,574,551,197,193,194,195,196,192,627,626,630,628,629,631,705,702,704,703,700,701,699,657,659,658,653,656,654,655,78,320,327,242,400,297,219,108,394,94,491,461,305,484,115,212,60,226,58,79,321,328,59,243,401,298,220,109,395,95,486,456,300,485,116,213,61,227,80,322,329,54,244,396,299,221,110,390,90,487,457,301,480,117,214,62,222,81,323,324,55,245,397,294,216,111,391,91,488,458,302,481,118,215,63,223,82,318,325,56,240,398,295,217,112,392,92,489,459,303,482,119,210,64,224,57,83,319,326,241,399,296,218,113,393,93,490,460,304,483,114,211,65,225,74,76,77,72,73,75,663,670,671,664,669,661,650,646,648,649,652,647,651,679,678,681,680,682,684,683,311,314,466,424,251,11,12,442,479,380,497,428,352,407,434,252,362,238,230,306,315,467,231,425,246,6,13,443,475,381,492,429,353,402,435,253,363,239,307,316,462,232,420,247,7,14,438,474,382,493,430,348,403,436,254,364,234,308,317,463,233,421,248,8,15,439,476,383,494,431,349,404,437,255,365,235,309,312,464,228,422,249,9,16,440,477,378,495,426,350,405,432,256,360,236,229,310,313,465,423,250,10,17,441,478,379,496,427,351,406,433,257,361,237,415,417,418,419,414,416,673,667,668,665,666,672,642,640,635,637,641,636,639,696,688,691,698,697,686,690,147,289,534,535,538,536,532,537,131,103,334,455,265,448,376,386,85,122,533,148,290,541,540,542,545,543,539,544,126,104,335,450,266,449,377,387,86,123,149,291,506,504,507,510,508,505,509,127,105,330,451,267,444,372,388,87,124,144,292,513,511,514,517,515,512,516,128,106,331,452,268,445,373,389,88,125,145,293,520,518,521,524,522,519,523,129,107,332,453,269,446,374,384,89,120,525,146,288,527,528,531,529,526,530,130,102,333,454,264,447,375,385,84,121,205,207,208,209,204,206,674,660,662,675,677,676,634,633,643,644,645,632,638,687,694,693,695,689,692,685,203,32,40,2,71,29,47,136,100,281,22,472,366,138,274,48,282,342,259,198,33,41,260,3,66,24,42,137,101,276,23,473,367,139,275,49,283,343,199,34,36,261,4,67,25,43,132,96,277,18,469,368,140,270,50,284,344,200,35,37,262,5,68,26,44,133,97,278,19,468,369,141,271,51,285,345,201,30,38,263,1,69,27,45,134,98,279,20,470,370,142,272,52,286,346,258,202,31,39,0,70,28,46,135,99,280,21,471,371,143,273,53,287,347,501,503,502,499,500,498,606,609,610,607,611,608,617,612,614,618,613,615,616,624,619,622,620,623,621,625 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#4200f14c740e474f3dea205eb4441577a1bf3df807bed6999bfa1c5fad1f3a90, M = {0, 20, 40, 61, 80, 102, 127} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-06 16:32:31 · history