Equation 677 Database

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Magma f1405eb611fc…

magma f1405eb611fc
Size
720
Isomorphism class hash
f1405eb611fcf4bd555ea80257c4961eed25c244209c0d0ce0f4b5503a0d7141
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
2026-10-08 02:46:48
Display reorder
64,65,66,67,68,69,70,71,72,58,59,60,61,62,63,719,557,604,584,558,605,585,559,606,586,560,607,587,561,608,588,562,609,589,563,610,590,564,611,591,565,612,592,566,598,593,567,599,594,553,600,595,554,601,596,555,602,597,583,556,603,581,573,574,575,576,577,578,579,580,568,569,570,571,572,582,678,676,677,675,319,365,344,320,366,345,321,367,346,322,368,347,323,369,348,324,370,349,325,371,350,326,372,351,327,358,352,313,359,353,314,360,354,315,361,355,316,362,356,317,363,357,343,318,364,342,334,335,336,337,338,339,340,341,329,330,331,332,333,328,704,705,703,706,657,637,617,643,638,618,644,639,619,645,640,620,646,641,621,647,642,622,648,628,623,649,629,624,650,630,625,651,631,626,652,632,627,653,633,613,654,634,614,655,635,615,616,656,636,6,13,14,15,2,1,3,4,5,8,9,10,11,12,7,684,685,683,686,391,386,432,392,387,418,393,373,419,394,374,420,395,375,421,396,376,422,397,377,423,398,378,424,399,379,425,400,380,426,401,381,427,402,382,428,388,383,429,389,384,430,431,390,385,414,406,407,408,409,410,411,412,413,416,417,403,404,405,415,692,694,691,693,173,153,133,174,154,134,175,155,135,176,156,136,177,157,137,163,158,138,164,159,139,165,160,140,166,161,141,167,162,142,168,148,143,169,149,144,170,150,145,171,151,146,147,172,152,181,188,189,190,191,192,178,179,180,183,184,185,186,187,182,680,682,679,681,674,671,672,673,31,45,659,32,46,660,33,47,661,34,48,662,35,49,663,36,50,664,37,51,665,38,52,666,39,53,667,40,54,668,41,55,669,42,56,670,43,57,0,658,44,28,20,21,22,23,24,25,26,27,30,16,17,18,19,29,709,708,710,707,84,130,110,85,131,111,86,132,112,87,118,113,73,119,114,74,120,115,75,121,116,76,122,117,77,123,103,78,124,104,79,125,105,80,126,106,81,127,107,82,128,108,109,83,129,92,99,100,101,102,88,89,90,91,94,95,96,97,98,93,717,716,718,715,249,229,208,250,230,209,251,231,210,252,232,211,238,233,212,239,234,213,240,235,214,241,236,215,242,237,216,243,223,217,244,224,218,245,225,219,246,226,220,247,227,221,222,248,228,206,198,199,200,201,202,203,204,205,193,194,195,196,197,207,713,712,714,711,505,551,531,506,552,532,507,538,533,493,539,534,494,540,535,495,541,536,496,542,537,497,543,523,498,544,524,499,545,525,500,546,526,501,547,527,502,548,528,503,549,529,530,504,550,514,521,522,508,509,510,511,512,513,516,517,518,519,520,515,688,689,687,690,263,310,290,264,311,291,265,312,292,266,298,293,267,299,294,253,300,295,254,301,296,255,302,297,256,303,283,257,304,284,258,305,285,259,306,286,260,307,287,261,308,288,289,262,309,271,278,279,280,281,282,268,269,270,273,274,275,276,277,272,698,697,696,695,475,454,433,476,455,434,477,456,435,463,457,436,464,458,437,465,459,438,466,460,439,467,461,440,468,462,441,469,448,442,470,449,443,471,450,444,472,451,445,473,452,446,447,474,453,484,491,492,478,479,480,481,482,483,486,487,488,489,490,485,702,700,701,699 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#9916b9303e5777c051d457f13e65b220048127e3f9475b765d37bfd24fd4df83, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 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 2026-10-08 02:46:49 · history