Equation 677 Database

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Magma 286b0419d058…

magma 286b0419d058
Size
720
Isomorphism class hash
286b0419d058b86d54b04d5542ddc1fb0d900a27c49faaf265026d2e42ac5831
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 20:58:57
Display reorder
49,50,51,52,53,54,55,56,57,43,44,45,46,47,48,719,551,589,572,552,590,573,538,591,574,539,592,575,540,593,576,541,594,577,542,595,578,543,596,579,544,597,580,545,583,581,546,584,582,547,585,568,548,586,569,549,587,570,571,550,588,554,561,562,563,564,565,566,567,553,556,557,558,559,560,555,678,676,677,675,411,394,376,412,395,377,413,396,378,414,397,379,415,398,380,416,399,381,417,400,382,403,401,383,404,402,384,405,388,385,406,389,386,407,390,387,408,391,373,409,392,374,375,410,393,359,366,367,368,369,370,371,372,358,361,362,363,364,365,360,704,705,703,706,657,640,621,643,641,622,644,642,623,645,628,624,646,629,625,647,630,626,648,631,627,649,632,613,650,633,614,651,634,615,652,635,616,653,636,617,654,637,618,655,638,619,620,656,639,603,610,611,612,598,599,600,601,602,605,606,607,608,609,604,684,685,683,686,156,138,120,157,139,121,158,140,122,159,141,123,160,142,124,161,143,125,162,144,126,148,145,127,149,146,128,150,147,129,151,133,130,152,134,131,153,135,132,154,136,118,119,155,137,173,165,166,167,168,169,170,171,172,175,176,177,163,164,174,692,694,691,693,180,232,214,181,233,215,182,234,216,183,235,217,184,236,218,185,237,219,186,223,220,187,224,221,188,225,222,189,226,208,190,227,209,191,228,210,192,229,211,178,230,212,213,179,231,197,204,205,206,207,193,194,195,196,199,200,201,202,203,198,680,682,679,681,674,671,672,673,19,33,659,20,34,660,21,35,661,22,36,662,23,37,663,24,38,664,25,39,665,26,40,666,27,41,667,28,42,668,29,3,669,30,1,670,31,0,2,658,32,16,8,9,10,11,12,13,14,15,18,4,5,6,7,17,709,708,710,707,66,117,100,67,103,101,68,104,102,69,105,88,70,106,89,71,107,90,72,108,91,58,109,92,59,110,93,60,111,94,61,112,95,62,113,96,63,114,97,64,115,98,99,65,116,83,75,76,77,78,79,80,81,82,85,86,87,73,74,84,717,716,718,715,277,258,241,278,259,242,279,260,243,280,261,244,281,262,245,282,263,246,268,264,247,269,265,248,270,266,249,271,267,250,272,253,251,273,254,252,274,255,238,275,256,239,240,276,257,295,287,288,289,290,291,292,293,294,297,283,284,285,286,296,713,712,714,711,535,518,501,536,519,502,537,520,503,523,521,504,524,522,505,525,508,506,526,509,507,527,510,493,528,511,494,529,512,495,530,513,496,531,514,497,532,515,498,533,516,499,500,534,517,484,491,492,478,479,480,481,482,483,486,487,488,489,490,485,688,689,687,690,332,315,298,333,316,299,334,317,300,335,318,301,336,319,302,337,320,303,338,321,304,339,322,305,340,323,306,341,324,307,342,325,308,328,326,309,329,327,310,330,313,311,312,331,314,350,357,343,344,345,346,347,348,349,352,353,354,355,356,351,698,697,696,695,427,467,448,428,468,449,429,469,450,430,470,451,431,471,452,432,472,453,418,473,454,419,474,455,420,475,456,421,476,457,422,477,458,423,463,459,424,464,460,425,465,461,462,426,466,445,437,438,439,440,441,442,443,444,447,433,434,435,436,446,702,700,701,699 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 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#5ea0801c37b7140a4d0f8cc6cd6f875b6a59b1b3f8cb66e6f780ccb36bd56c74, M = {0, 4, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 52, 58, 75} 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 2026-10-06 20:58:58 · history