Equation 677 Database

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Magma c1c4ba842be8…

magma c1c4ba842be8
Size
707
Isomorphism class hash
c1c4ba842be8448ea0ea2955e2361f5c54a4f7d0b7c6e61ebc5a4a25b5e22fbc
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 10:25:41
Display reorder
565,566,564,568,569,567,636,229,228,230,231,232,233,161,158,156,157,160,159,198,203,199,200,201,202,73,72,74,75,76,77,65,64,60,61,62,63,220,219,221,216,217,218,39,38,40,41,36,37,34,33,35,30,31,32,42,47,43,44,45,46,224,223,225,226,227,222,312,313,314,315,316,317,397,396,395,398,399,400,403,402,401,405,406,404,563,562,561,560,558,559,359,358,357,355,356,354,342,344,343,346,347,345,364,363,365,360,361,362,384,509,385,388,386,387,411,410,412,407,408,409,494,496,495,491,492,493,611,608,607,609,610,606,637,645,647,698,665,675,700,679,697,696,686,702,705,706,51,50,52,53,48,49,250,247,251,246,249,248,257,256,252,253,254,255,288,289,290,291,292,293,149,148,144,145,146,147,287,285,286,283,284,282,20,19,21,22,23,18,153,152,154,155,150,151,13,12,14,15,16,17,56,55,57,58,59,54,125,124,120,121,122,123,449,451,450,453,454,452,520,519,521,517,516,518,417,416,418,413,414,415,500,502,501,499,497,498,460,459,458,455,456,457,423,422,424,419,420,421,462,461,463,466,464,465,589,590,588,593,591,592,522,523,524,526,527,525,625,621,626,622,649,648,642,624,640,682,681,688,683,660,667,668,670,680,687,699,237,236,238,239,234,235,135,132,136,137,134,133,264,265,266,267,268,269,296,294,297,298,299,295,84,89,85,86,87,88,0,1,2,3,4,5,197,196,192,193,194,195,98,97,99,100,101,96,258,263,259,260,261,262,142,141,143,138,139,140,94,93,95,90,91,92,549,551,550,546,548,547,543,545,544,542,541,540,447,446,448,443,444,445,579,581,580,578,577,576,604,603,605,602,601,600,370,369,371,366,367,368,552,553,554,557,555,556,390,389,391,392,393,394,586,585,587,582,584,583,630,646,633,644,631,638,623,641,643,693,676,690,694,658,671,678,661,692,684,701,106,105,107,102,103,104,189,186,190,191,188,187,241,240,242,243,244,245,307,306,308,309,310,311,181,180,182,183,184,185,302,300,303,304,305,301,24,29,25,26,27,28,176,175,177,178,179,174,204,209,205,206,207,208,119,118,114,115,116,117,108,113,109,110,111,112,536,534,535,537,538,539,477,476,478,473,474,475,574,573,575,571,570,572,468,467,469,470,471,472,425,427,426,429,430,428,512,510,511,514,515,513,528,529,530,533,531,532,481,480,479,483,484,482,597,599,598,595,594,596,614,627,629,613,628,612,639,651,650,704,672,677,703,663,669,685,664,691,689,695,275,274,271,270,272,273,215,212,210,211,214,213,8,7,9,10,11,6,278,276,279,280,281,277,326,328,327,324,325,329,131,130,126,127,128,129,67,66,68,69,70,71,321,320,322,323,319,318,165,164,166,167,162,163,82,81,83,78,79,80,171,170,172,173,168,169,433,432,431,434,435,436,488,490,489,487,485,486,331,332,330,335,333,334,380,379,378,382,383,381,353,352,351,348,349,350,376,375,377,372,373,374,341,340,339,336,337,338,441,440,442,437,438,439,504,503,505,507,508,506,617,615,620,619,618,616,635,634,632,673,656,657,666,654,653,655,652,662,659,674 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#96b028d3c6de0cbaff964417289f690895c6af42769867ad5a7d2affbed8a752, M = {90, 91, 92, 93, 94, 95, 131} 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 10:25:43 · history