Equation 677 Database

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Magma ad3437971e3f…

magma ad3437971e3f
Size
705
Isomorphism class hash
ad3437971e3f82c53f120262ecf3bb516ff41df75504a2459d718a80be4546e0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 20:39:16
Display reorder
660,491,8,89,26,376,9,27,492,90,377,7,30,493,91,378,11,31,490,88,375,12,33,488,86,373,10,35,489,87,374,95,482,34,6,367,96,483,36,4,368,97,484,32,5,369,485,94,25,2,370,486,92,28,3,371,487,93,29,0,372,668,662,672,666,587,165,261,503,364,163,504,588,259,365,164,505,589,260,366,168,502,586,264,363,166,500,584,262,361,167,501,585,263,362,267,578,494,171,355,265,579,495,169,356,266,580,496,170,357,581,270,497,174,358,582,268,498,172,359,583,269,499,173,360,685,686,688,689,527,19,77,575,419,20,576,528,78,420,21,577,529,79,421,22,574,526,76,418,23,572,524,74,416,24,573,525,75,417,83,518,566,17,410,84,519,567,18,411,85,520,568,16,412,521,82,569,13,413,522,80,570,14,414,523,81,571,15,415,664,663,669,667,116,180,288,515,281,178,516,117,286,282,179,517,118,287,280,176,514,119,284,277,177,512,120,285,278,175,513,121,283,279,294,114,506,186,272,292,115,507,184,273,293,113,508,185,271,110,290,509,182,275,111,291,510,183,276,112,289,511,181,274,673,678,679,675,479,191,304,132,599,192,133,480,305,600,190,131,481,306,601,187,128,478,303,598,188,129,476,301,596,189,130,477,302,597,295,470,123,197,590,296,471,124,198,591,297,472,122,196,592,473,298,126,193,593,474,299,127,194,594,475,300,125,195,595,670,671,661,665,460,73,388,532,551,71,530,458,389,552,72,531,459,390,553,69,535,463,387,550,70,533,461,385,548,68,534,462,386,549,379,466,538,64,542,380,464,536,62,543,381,465,537,63,544,469,382,541,67,545,467,383,539,65,546,468,384,540,66,547,694,698,697,695,152,50,43,156,623,51,655,654,653,652,52,657,656,659,658,53,38,153,42,620,54,39,154,40,621,55,37,155,41,622,49,150,161,56,615,47,151,162,57,616,48,149,160,58,614,146,45,157,59,618,147,46,158,60,619,148,44,159,61,617,704,703,701,702,334,102,646,443,647,103,444,335,648,649,101,445,336,651,650,98,442,333,645,644,99,440,331,640,641,100,441,332,643,642,392,340,434,108,397,393,341,435,109,395,394,342,436,107,396,339,391,437,104,1,337,637,438,105,636,338,638,439,106,639,699,700,696,693,431,250,633,321,138,251,319,432,634,139,252,320,433,635,137,249,324,430,632,134,247,322,428,630,135,248,323,429,631,136,624,422,327,256,144,625,423,325,257,145,626,424,326,258,143,425,627,330,255,140,426,628,328,253,141,427,629,329,254,142,684,681,683,676,407,351,611,563,455,349,564,408,612,456,350,565,409,613,457,354,562,406,610,454,352,560,404,608,452,353,561,405,609,453,602,398,554,346,446,603,399,555,347,447,604,400,556,348,448,401,605,557,345,449,402,606,558,343,450,403,607,559,344,451,682,677,680,674,237,316,226,201,221,317,199,235,227,222,318,200,236,228,220,315,204,240,225,217,313,202,238,223,218,314,203,239,224,219,232,243,207,307,212,233,241,205,308,213,234,242,206,309,211,246,231,210,310,215,244,229,208,311,216,245,230,209,312,214,687,690,692,691 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#c8b00e8ba82c54826bf93ef2b9b2d8eeb61b8eb7ac0797b661231f1bb38e050b, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 20:39:17 · history