Equation 677 Database

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Magma 6cbf3df1a076…

magma 6cbf3df1a076
Size
707
Isomorphism class hash
6cbf3df1a0763997be21b55c56c9d24c2e4d5ba782269694d1c5d2f3bae24b8b
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 19:17:08
Display reorder
601,600,602,603,604,605,706,594,528,83,548,543,96,554,562,585,567,537,188,581,591,571,95,84,72,70,595,572,530,81,546,544,97,553,563,586,568,538,186,579,592,93,85,71,73,596,570,529,82,547,545,98,552,561,587,569,539,187,580,593,94,86,69,74,558,99,582,565,535,191,578,588,574,597,532,80,551,541,557,75,67,87,92,555,100,560,583,564,534,189,576,589,575,598,533,78,549,540,76,68,90,88,101,559,556,584,566,536,190,577,590,573,599,531,79,550,542,91,77,66,89,105,106,104,102,103,107,673,675,672,674,677,676,629,628,630,627,626,632,631,703,699,705,702,704,700,701,344,525,513,504,491,192,128,493,32,48,516,501,364,340,354,417,109,136,18,343,356,526,514,505,489,193,126,494,30,49,518,502,365,341,418,110,19,137,342,355,527,515,506,490,194,127,492,31,50,517,503,363,336,419,108,20,135,496,195,35,51,520,498,360,337,358,347,523,510,507,488,131,133,21,112,415,129,196,497,33,52,521,499,362,338,359,345,522,511,508,487,134,22,414,113,197,495,130,34,53,519,500,361,339,357,346,524,512,509,486,416,132,23,111,288,289,293,291,292,290,634,636,646,645,637,635,696,695,697,693,692,698,694,653,664,660,663,661,662,659,389,185,369,157,245,481,474,264,278,246,212,262,380,165,233,467,455,472,444,387,231,183,370,158,243,482,475,265,276,247,210,263,379,166,465,453,446,473,388,232,184,371,156,244,480,476,266,277,248,211,261,378,167,466,454,445,471,267,484,281,249,215,259,383,162,230,386,182,367,160,242,477,469,448,452,464,478,485,268,279,250,213,260,381,163,228,385,180,366,161,240,470,449,462,450,483,269,479,280,251,214,258,382,164,229,384,181,368,159,241,463,468,447,451,456,457,461,459,460,458,638,643,650,644,649,648,684,682,680,679,683,678,681,669,668,666,671,667,665,670,225,255,372,429,434,154,272,440,217,0,237,420,177,282,170,393,406,398,408,226,168,256,374,430,432,155,270,438,218,2,238,422,178,283,394,407,410,397,227,169,257,373,431,433,153,271,439,216,1,239,421,179,284,395,405,409,396,443,151,220,4,234,424,174,285,173,222,252,376,427,437,275,401,412,402,391,273,152,441,221,5,235,425,175,286,171,223,253,377,426,435,399,413,390,404,150,442,274,219,3,236,423,176,287,172,224,254,375,428,436,392,400,411,403,349,348,353,351,352,350,647,642,633,639,640,641,690,689,691,685,688,687,686,651,658,657,655,656,654,652,42,24,321,60,313,295,199,144,41,10,12,142,119,59,121,309,335,209,305,43,122,25,322,61,312,296,200,145,39,11,13,143,117,57,310,333,303,207,44,120,26,323,62,314,294,198,146,40,9,14,141,118,58,311,334,304,208,147,298,38,7,15,139,116,56,124,45,27,319,63,315,202,206,302,332,307,203,299,148,36,8,16,140,114,54,125,46,28,318,64,316,204,301,306,331,297,149,201,37,6,17,138,115,55,123,47,29,320,65,317,308,205,300,330,329,327,324,326,325,328,609,622,617,615,623,618,610,616,619,611,614,621,612,620,613,608,606,624,607,625 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#a8026a02368cc98eace7a76910bb242dec082e21ec6371f1fc7226b87fb07666, M = {8, 29, 49, 62, 83, 103, 135} 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 19:17:09 · history