Equation 677 Database

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Magma 78ad28ffb7b3…

magma 78ad28ffb7b3
Size
705
Isomorphism class hash
78ad28ffb7b3e3c3f2fe1c505ca41f3f766bacc0300e894b2382f8749a634218
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 19:07:40
Display reorder
660,380,78,64,386,86,79,84,378,65,384,85,80,379,63,385,77,82,383,67,389,83,75,381,68,387,81,76,382,66,388,92,69,375,62,392,90,70,376,60,390,391,91,71,377,61,72,88,374,58,395,59,73,89,372,393,74,87,373,57,394,685,686,688,687,212,192,231,29,459,193,460,210,232,27,461,194,211,233,28,191,458,208,234,32,456,189,209,235,30,457,190,207,236,31,465,198,203,229,24,466,199,201,230,25,26,467,200,202,228,197,464,206,225,23,226,195,462,204,21,196,463,205,227,22,701,702,704,703,597,579,623,603,371,580,369,598,621,604,370,581,599,622,605,578,367,596,619,602,368,576,594,620,600,366,577,595,618,601,362,585,588,614,609,360,586,589,612,610,611,361,587,590,613,584,365,591,617,608,615,582,363,592,606,583,364,593,616,607,670,669,672,671,273,263,259,240,469,261,470,274,260,241,468,262,275,258,242,266,472,276,255,239,473,264,277,256,237,471,265,278,257,238,475,269,279,250,246,476,267,280,251,247,248,474,268,281,249,272,478,282,253,245,254,270,479,283,243,271,477,284,252,244,680,677,679,678,288,503,487,307,14,501,12,289,488,308,13,502,290,486,306,499,10,287,490,303,11,500,285,491,304,9,498,286,489,305,20,494,294,485,298,18,492,295,483,299,297,19,493,296,484,497,16,293,481,301,482,495,17,291,302,496,15,292,480,300,689,690,691,692,53,562,547,149,324,563,325,51,548,147,326,561,52,546,148,558,323,56,550,152,321,559,54,551,150,322,560,55,549,151,330,553,48,545,144,331,554,49,543,145,146,332,552,50,544,556,329,47,541,143,542,557,327,45,141,555,328,46,540,142,697,698,700,699,117,107,647,630,103,105,104,118,645,631,102,106,119,646,632,110,99,120,643,633,100,108,121,644,634,101,109,122,642,635,94,113,123,638,628,95,111,124,636,629,627,93,112,125,637,116,97,126,641,624,639,114,98,127,625,115,96,128,640,626,661,662,664,663,443,423,419,399,158,424,156,441,417,400,157,425,442,418,401,422,154,439,415,398,155,420,440,416,396,153,421,438,414,397,164,429,434,410,405,162,430,432,408,406,407,163,431,433,409,428,160,437,413,404,411,426,161,435,402,427,159,436,412,403,682,681,684,683,5,353,342,338,565,351,566,3,343,336,564,352,4,344,337,356,568,8,345,341,569,354,6,346,339,567,355,7,347,340,571,655,653,654,652,572,659,657,658,656,649,570,650,648,651,359,574,2,350,335,348,357,575,1,333,358,573,0,349,334,693,694,696,695,319,531,527,511,133,532,134,320,525,512,132,533,318,526,510,530,129,315,523,514,130,528,316,524,515,131,529,317,522,513,139,537,310,518,509,140,538,311,516,507,508,138,539,309,517,536,135,313,521,505,519,534,136,314,506,535,137,312,520,504,666,665,668,667,171,34,452,187,219,35,220,172,450,188,221,33,173,451,186,37,222,174,455,183,223,38,175,453,184,224,36,176,454,185,217,40,169,447,178,218,41,170,448,179,177,216,39,168,449,43,213,165,446,181,444,44,214,166,182,42,215,167,445,180,674,673,676,675 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#87aba77d55a93960597d69a42bda986d959be94fa8d2c920629e2ba026b38a72, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 19:07:41 · history