Equation 677 Database

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Magma 501eeacf03df…

magma 501eeacf03df
Size
707
Isomorphism class hash
501eeacf03df7ae328a3d8b33347d40bafcb1a231935a8b953a7139f2b4e3461
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 10:26:07
Display reorder
603,604,605,601,600,602,706,594,269,550,540,255,275,234,554,569,582,558,248,571,593,581,14,244,539,277,595,579,267,551,542,256,273,235,553,567,583,560,246,572,591,12,245,278,537,596,580,268,549,541,257,274,236,552,568,584,559,247,570,592,13,243,276,538,237,272,557,566,585,562,251,574,590,578,597,266,546,544,252,536,280,241,17,270,238,555,565,586,563,249,575,588,576,598,264,548,545,253,535,281,15,242,271,239,556,564,587,561,250,573,589,577,599,265,547,543,254,16,534,279,240,261,262,260,258,259,263,677,676,673,672,675,674,626,627,632,630,631,628,629,701,703,700,699,702,705,704,11,423,308,287,352,304,26,342,288,448,396,327,395,376,22,1,507,440,368,9,23,424,306,285,353,305,24,343,289,449,397,328,393,377,0,508,366,438,10,21,425,307,286,351,303,25,344,290,447,398,329,394,375,2,509,367,439,29,301,345,291,445,399,324,392,373,19,8,420,311,284,349,443,371,505,3,302,27,346,292,446,400,325,390,374,20,6,421,309,282,350,441,369,4,504,300,28,347,293,444,401,326,391,372,18,7,422,310,283,348,5,442,370,506,417,418,416,414,415,419,641,644,639,650,648,646,695,693,690,691,687,686,697,661,663,658,671,669,664,667,67,135,201,531,36,194,173,46,113,524,92,516,88,220,174,65,152,77,224,68,175,136,202,532,37,192,171,47,111,523,90,518,89,221,63,150,222,75,66,176,137,203,533,38,193,172,45,112,522,91,517,87,219,64,151,223,76,170,197,43,110,527,95,520,85,217,177,70,132,198,529,39,74,227,155,62,195,168,44,108,525,93,521,86,218,178,71,133,199,528,40,72,225,60,153,196,169,42,109,526,94,519,84,216,179,69,134,200,530,41,61,73,226,154,129,130,128,126,127,131,642,649,643,647,638,645,679,681,684,678,683,680,682,654,651,655,657,652,656,653,215,232,182,83,120,190,164,118,497,138,56,30,51,96,159,204,500,149,106,213,160,233,180,81,121,191,162,119,494,139,54,31,52,97,205,499,107,147,214,161,231,181,82,122,189,163,117,492,140,55,32,53,98,206,498,105,148,167,187,115,493,141,59,33,48,99,156,212,229,185,80,123,146,103,503,207,188,165,116,495,142,57,34,49,100,157,210,230,183,78,124,144,104,208,501,186,166,114,496,143,58,35,50,101,158,211,228,184,79,125,209,145,102,502,512,511,514,515,513,510,635,633,637,634,640,636,692,685,696,688,689,694,698,659,660,665,670,662,666,668,455,335,382,488,456,386,412,469,479,320,430,361,432,484,404,465,359,316,296,453,402,333,383,487,458,384,413,468,477,318,431,362,433,485,466,357,294,317,454,403,334,381,486,457,385,411,470,478,319,429,360,434,483,467,358,295,315,409,389,471,476,323,427,364,435,480,407,452,332,379,491,460,313,299,356,463,387,410,472,475,321,428,365,436,482,405,451,330,380,489,461,314,297,462,354,388,408,473,474,322,426,363,437,481,406,450,331,378,490,459,464,312,298,355,339,340,338,336,337,341,625,613,620,621,609,608,607,624,615,610,619,623,618,616,612,617,614,622,611,606 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 = {6, 27, 47, 75, 80, 102, 141} 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 10:26:08 · history