Equation 677 Database

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Magma 1b6ad6605b8e…

magma 1b6ad6605b8e
Size
707
Isomorphism class hash
1b6ad6605b8ed5b6419cb6dce84db32236fa8ccef9c770f19fbdfea75e3b1b74
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 08:51:36
Display reorder
115,114,116,117,118,119,706,32,34,35,30,31,33,140,139,141,142,143,138,332,330,333,334,335,331,320,319,321,322,323,318,305,304,300,301,302,303,316,315,317,312,313,314,164,163,165,166,167,162,144,149,145,146,147,148,16,15,17,12,13,14,172,171,173,168,169,170,186,191,187,188,189,190,505,504,503,502,500,501,493,492,491,490,567,489,350,349,348,352,353,351,336,337,338,340,341,339,587,586,585,584,583,582,455,457,456,459,460,458,471,470,469,467,468,466,515,517,516,514,512,513,357,359,358,356,354,355,608,620,623,622,626,627,649,638,644,698,667,663,662,684,702,699,695,700,705,703,156,158,159,160,161,157,46,45,47,42,43,44,217,216,221,218,220,219,226,225,227,223,222,224,207,206,208,209,204,205,112,111,113,108,109,110,107,106,102,103,104,105,93,92,94,95,90,91,229,228,230,231,232,233,99,98,100,101,96,97,18,23,19,20,21,22,430,429,428,427,425,426,364,363,365,361,362,360,421,420,419,423,424,422,599,598,597,596,595,594,417,416,418,414,415,413,385,384,386,388,387,568,573,575,572,570,571,569,531,530,532,533,536,537,566,565,564,557,555,556,609,606,607,630,631,624,637,639,636,689,680,676,656,665,682,677,673,681,701,694,84,86,87,88,89,85,291,290,292,293,288,289,10,9,11,6,7,8,63,62,64,65,60,61,277,276,278,279,280,281,273,272,274,275,270,271,210,215,211,212,213,214,82,81,83,78,79,80,260,259,261,262,263,258,50,49,51,52,53,48,198,203,199,200,201,202,563,562,561,560,558,559,401,403,402,404,405,406,409,408,407,411,412,410,507,506,508,510,511,509,434,436,435,431,432,433,392,394,393,390,391,389,378,380,379,383,381,382,539,538,540,541,542,543,527,529,528,526,524,525,625,632,628,633,634,635,643,619,642,696,679,678,659,669,691,690,661,687,692,693,257,253,254,255,256,252,329,328,324,325,326,327,128,127,129,130,131,126,174,179,175,176,177,178,184,183,185,180,181,182,73,72,74,75,76,77,296,295,297,298,299,294,3,2,4,5,1,0,241,240,242,243,244,245,122,121,123,124,125,120,66,71,67,68,69,70,439,438,437,442,440,441,576,578,577,579,580,581,518,520,519,523,521,522,374,373,372,377,375,376,368,367,366,371,369,370,546,545,544,547,574,548,592,591,593,588,589,590,601,600,602,603,604,605,446,448,447,445,443,444,641,647,640,646,650,629,645,621,648,704,671,668,674,670,683,688,666,686,697,685,133,135,136,137,132,134,194,193,195,196,197,192,25,24,26,27,28,29,155,154,150,151,152,153,248,247,249,250,251,246,236,235,237,238,239,234,58,57,59,54,55,56,39,38,40,41,36,37,266,265,267,268,269,264,286,285,287,282,283,284,309,308,310,311,306,307,450,449,451,453,454,452,551,549,550,554,552,553,494,496,495,499,497,498,346,345,347,343,344,342,399,398,400,396,397,395,472,474,473,476,477,475,488,487,486,484,485,483,482,481,480,479,535,478,465,464,534,461,462,463,616,617,618,613,615,612,610,611,614,675,653,652,651,655,657,658,654,660,672,664 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#10604212f7d4a7b51fd21a22d9c743e5a67297285884dbf7fd2d260472af6645, M = {48, 49, 50, 51, 52, 53, 138} 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 08:51:37 · history