Equation 677 Database

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Magma 4da6c59960c5…

magma 4da6c59960c5
Size
705
Isomorphism class hash
4da6c59960c5f7e433b3348ea6ef53c1a4934e3009921e723d644d55f97f60c7
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 17:23:33
Display reorder
660,621,635,629,23,634,640,654,21,649,655,22,615,601,609,614,541,555,19,549,554,561,575,20,569,574,580,594,18,589,595,450,442,14,448,451,475,461,12,469,474,434,420,13,429,435,502,514,17,509,515,522,534,15,529,535,482,494,16,489,495,690,693,702,701,624,622,632,154,623,644,642,155,652,643,153,602,604,612,603,544,542,150,552,543,564,562,151,572,563,584,582,152,592,583,443,445,145,449,444,462,464,146,472,463,422,424,144,432,423,504,501,148,512,503,524,521,149,532,523,484,480,147,492,483,696,697,700,699,418,262,358,70,394,419,263,71,359,395,69,261,417,357,393,414,258,66,354,390,415,259,67,355,391,416,260,68,356,392,253,409,61,349,385,254,410,62,350,386,252,408,60,348,384,412,256,64,352,388,413,257,65,353,389,411,255,63,351,387,674,667,670,662,346,334,406,126,322,347,335,127,407,323,128,333,345,405,321,342,330,129,402,318,343,331,130,403,319,344,332,131,404,320,325,337,124,397,313,326,338,125,398,314,324,336,123,396,312,340,328,120,400,316,341,329,121,401,317,339,327,122,399,315,666,671,661,663,638,639,627,5,625,658,659,3,647,645,4,619,618,607,605,558,559,0,547,545,578,579,2,567,565,598,599,1,587,585,458,459,11,447,446,478,479,9,467,465,438,439,10,427,425,519,518,7,507,505,539,538,8,527,525,499,498,6,487,485,694,688,686,689,633,620,628,309,630,653,641,310,648,650,311,600,613,608,610,553,540,308,548,550,573,560,306,568,570,593,581,307,588,590,456,457,300,440,441,460,473,301,468,470,421,433,302,428,430,513,500,303,508,510,533,520,304,528,530,493,481,305,488,490,685,692,695,698,631,626,636,45,637,651,646,46,656,657,47,606,611,617,616,551,546,44,557,556,571,566,42,576,577,591,586,43,596,597,454,455,36,452,453,466,471,37,476,477,426,431,38,437,436,511,506,39,517,516,531,526,40,536,537,491,486,41,497,496,691,703,704,687,140,73,94,232,248,138,74,233,95,246,231,72,139,93,247,143,76,228,90,251,141,77,229,91,249,142,75,230,92,250,79,135,238,85,243,80,136,239,86,244,78,137,237,84,245,134,82,234,88,242,132,83,235,89,240,133,81,236,87,241,680,664,675,677,109,382,30,268,103,110,383,269,31,104,267,381,108,32,102,112,378,264,33,106,113,379,265,34,107,111,380,266,35,105,373,115,274,28,101,374,116,275,29,99,372,114,273,27,100,118,376,270,24,97,119,377,271,25,98,117,375,272,26,96,678,681,682,669,191,157,178,54,370,189,158,55,179,371,56,156,190,177,369,187,160,57,174,366,188,161,58,175,367,186,159,59,176,368,163,182,52,169,361,164,180,53,170,362,162,181,51,168,360,185,166,48,172,364,183,167,49,173,365,184,165,50,171,363,683,665,668,684,201,214,284,216,289,202,215,217,282,290,218,213,203,283,288,200,210,219,287,292,198,211,220,285,293,199,212,221,286,291,205,192,222,279,295,206,193,223,280,296,204,194,224,281,294,195,208,225,278,298,196,209,226,276,299,197,207,227,277,297,673,676,672,679 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#51b008b28ab03bd312921cf92cf8265fda62df0fbe14e18f3974b5c43c79b0a4, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 17:23:33 · history