Equation 677 Database

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Magma ab29c336a75a…

magma ab29c336a75a
Size
705
Isomorphism class hash
ab29c336a75abbae749cdff9905660d12efd4d9480a7bdb251a34711163c22cc
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 21:08:15
Display reorder
660,34,89,284,95,277,35,90,282,96,278,36,88,283,94,276,92,37,287,98,280,93,38,285,99,281,91,39,286,97,279,40,290,87,101,275,41,288,85,102,273,42,289,86,100,274,293,43,83,104,271,291,44,84,105,272,292,45,82,103,270,685,686,688,687,144,402,397,169,32,142,403,398,170,33,143,404,396,171,31,405,147,400,168,28,406,145,401,166,29,407,146,399,167,30,150,395,408,175,23,148,393,409,176,24,149,394,410,177,22,391,153,411,174,26,392,151,412,172,27,390,152,413,173,25,701,702,704,703,258,547,585,567,569,259,548,583,565,570,260,549,584,566,568,546,261,581,563,572,544,262,582,564,573,545,263,580,562,571,264,591,553,558,575,265,589,554,556,576,266,590,555,557,574,587,267,552,561,578,588,268,550,559,579,586,269,551,560,577,670,669,672,671,137,188,437,190,420,138,189,435,191,421,136,187,436,192,422,184,140,433,193,423,185,141,434,194,424,186,139,432,195,425,135,428,179,196,418,133,426,180,197,419,134,427,178,198,417,431,131,182,199,414,429,132,183,200,415,430,130,181,201,416,680,677,679,678,207,485,465,449,450,205,483,466,447,451,206,484,467,448,452,481,203,464,445,453,482,204,462,446,454,480,202,463,444,455,213,471,476,440,456,211,472,474,438,457,212,473,475,439,458,470,209,479,443,459,468,210,477,441,460,469,208,478,442,461,689,690,691,692,229,60,53,74,528,230,58,54,75,529,231,59,52,73,530,63,228,56,70,531,61,226,57,71,532,62,227,55,72,533,235,51,66,80,526,236,49,64,81,527,237,50,65,79,525,47,234,69,76,522,48,232,67,77,523,46,233,68,78,524,697,698,700,699,601,614,651,617,631,602,615,649,618,632,603,613,650,616,633,610,600,647,620,630,611,598,648,621,628,612,599,646,619,629,592,642,605,623,637,593,640,606,624,638,594,641,604,622,639,645,595,608,626,636,643,596,609,627,634,644,597,607,625,635,661,662,664,663,117,340,321,305,306,115,341,322,303,307,116,339,323,304,308,336,113,320,301,309,337,114,318,302,310,338,112,319,300,311,108,327,331,296,312,106,328,332,294,313,107,329,330,295,314,326,111,334,299,315,324,109,335,297,316,325,110,333,298,317,682,681,684,683,120,20,539,242,249,118,21,540,243,247,119,19,538,241,248,16,123,542,245,252,17,121,543,246,250,18,122,541,244,251,126,659,658,657,656,124,537,12,257,253,125,654,653,652,655,535,129,14,239,256,536,127,15,240,254,534,128,13,238,255,693,694,696,695,6,512,508,224,492,7,510,509,225,493,8,511,507,223,494,515,9,504,220,495,513,10,505,221,496,514,11,506,222,497,4,499,518,215,490,5,500,516,216,491,3,498,517,214,489,502,1,521,218,486,503,0,519,219,487,501,2,520,217,488,666,665,668,667,154,381,367,345,365,155,382,368,346,363,156,383,366,347,364,380,157,370,344,361,378,158,371,342,362,379,159,369,343,360,160,373,387,351,356,161,374,388,352,354,162,372,389,353,355,376,163,386,350,359,377,164,384,348,357,375,165,385,349,358,674,673,676,675 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#d958d834958932013e293186c3edbca2299f39c5df5a243bf65f8d4f2fad3f22, 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 21:08:16 · history