Equation 677 Database

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Magma 93d9b678385b…

magma 93d9b678385b
Size
707
Isomorphism class hash
93d9b678385bb4805f1a1037b510ce75bc60863b46aa6888a557b0c10411760b
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
2026-10-08 19:01:25
Display reorder
601,600,602,603,604,605,706,568,159,558,173,595,163,545,556,152,588,456,444,570,582,577,550,463,535,532,569,578,160,560,171,596,164,543,557,150,589,457,445,571,583,551,464,533,534,567,576,161,559,172,594,162,544,555,151,590,458,446,572,584,549,462,531,536,552,166,155,591,459,447,573,585,580,564,156,562,170,598,542,537,528,466,546,541,167,554,153,592,460,448,574,586,581,566,157,563,168,599,538,530,548,467,165,553,540,154,593,461,449,575,587,579,565,158,561,169,597,547,539,529,465,177,178,176,174,175,179,677,675,676,672,673,674,627,628,632,631,629,630,626,704,702,699,701,700,703,705,244,221,486,356,274,306,328,281,223,13,373,330,9,195,302,264,348,381,248,245,303,219,488,357,275,307,326,282,224,14,371,331,10,196,265,349,246,382,243,304,220,487,358,273,305,327,283,222,12,372,329,11,197,266,347,247,380,284,309,226,16,376,333,6,192,299,241,218,490,353,271,325,378,251,351,267,323,310,285,227,17,374,334,7,193,300,242,216,491,354,272,379,249,268,352,308,286,324,225,15,375,332,8,194,301,240,217,489,355,270,269,377,250,350,202,203,198,199,200,201,641,645,649,640,643,647,696,686,690,694,698,687,692,668,670,665,667,669,671,666,394,482,477,468,129,91,107,1,69,33,418,109,38,54,89,134,437,420,396,392,87,481,478,470,130,92,105,0,70,34,416,110,36,55,132,438,397,421,393,88,480,479,469,131,90,106,2,71,35,417,108,37,56,133,439,395,419,3,94,66,30,415,112,41,57,86,391,485,475,472,126,104,423,399,440,137,102,95,4,67,31,413,113,39,58,84,389,483,474,473,127,424,400,135,441,93,5,103,68,32,414,111,40,59,85,390,484,476,471,128,136,422,398,442,48,49,53,51,52,50,639,642,644,646,648,650,678,679,680,681,682,684,683,657,651,652,653,654,655,656,507,524,410,42,74,511,427,403,99,145,123,435,141,63,27,81,498,116,519,508,28,523,411,43,72,510,425,401,100,146,124,436,142,64,82,500,520,114,509,29,522,412,44,73,512,426,402,101,144,125,434,143,65,83,499,521,115,406,513,96,148,120,432,138,60,24,505,527,407,45,77,430,119,517,502,78,428,514,404,97,149,121,433,139,61,25,504,525,408,46,75,117,516,79,503,515,405,429,98,147,122,431,140,62,26,506,526,409,47,76,80,118,518,501,493,492,497,495,496,494,633,636,638,634,637,635,695,688,693,685,691,697,689,664,661,663,658,659,662,660,256,342,455,181,204,364,289,21,338,315,232,296,319,387,366,214,189,236,258,257,367,343,454,182,205,362,287,22,339,316,233,297,317,388,215,190,259,234,255,365,341,450,180,206,363,288,23,340,314,231,298,318,386,213,191,260,235,18,361,335,312,229,293,322,384,369,253,345,453,184,207,292,239,261,186,211,290,359,19,336,313,230,294,320,385,370,254,346,451,185,208,237,262,212,187,360,20,291,337,311,228,295,321,383,368,252,344,452,183,209,210,238,263,188,443,279,277,278,276,280,608,611,607,609,610,612,615,616,613,606,617,614,618,623,624,619,625,621,620,622 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#a8026a02368cc98eace7a76910bb242dec082e21ec6371f1fc7226b87fb07666, M = {9, 30, 50, 63, 84, 104, 129} 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 2026-10-08 19:01:26 · history