Equation 677 Database

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Magma d021c56971ba…

magma d021c56971ba
Size
705
Isomorphism class hash
d021c56971ba900c5a7ca8668bd291050d17740b0686a863e1e0c6fc07fc196e
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 16:44:22
Display reorder
660,271,274,362,290,370,368,275,272,363,291,369,276,273,364,289,373,270,277,365,286,268,371,278,366,287,269,372,279,367,288,262,280,376,360,296,281,374,361,263,297,282,375,359,264,295,379,283,356,265,292,284,377,357,266,293,378,285,358,267,294,685,686,688,687,411,58,234,73,55,56,59,412,232,74,57,60,410,233,75,54,414,61,237,72,415,52,62,235,70,413,53,63,236,71,409,64,46,229,79,65,47,230,407,80,66,48,231,408,81,49,67,228,405,78,68,50,226,406,76,51,69,227,404,77,701,702,704,703,344,593,569,615,589,590,594,345,570,613,591,592,346,568,614,588,347,596,572,611,348,586,597,573,612,349,587,595,571,610,350,599,580,575,606,600,581,576,351,604,598,582,574,352,605,583,602,578,353,609,603,584,579,354,607,585,601,577,355,608,670,669,672,671,240,441,416,462,431,432,442,238,417,463,433,440,239,418,461,430,243,444,419,458,241,428,445,420,459,242,429,443,421,460,246,447,437,422,453,448,438,423,244,454,446,439,424,245,452,436,450,425,249,456,451,434,426,247,457,435,449,427,248,455,680,677,679,678,105,487,256,164,471,472,485,103,257,165,470,486,104,258,163,474,101,483,259,160,102,475,484,260,161,100,473,482,261,162,96,478,469,254,155,476,467,255,94,156,477,468,253,95,154,465,481,250,99,158,479,466,251,97,159,464,480,252,98,157,689,690,691,692,45,509,528,512,540,541,510,43,529,513,539,511,44,527,514,536,41,508,524,515,42,537,506,525,516,40,538,507,526,517,36,500,546,534,518,501,547,535,34,519,502,545,533,35,520,542,503,530,39,521,504,543,531,37,522,544,505,532,38,523,697,698,700,699,131,622,651,629,153,151,623,132,649,630,152,624,130,650,628,149,134,625,647,632,135,150,626,648,633,133,148,627,646,631,137,620,144,642,635,621,142,640,138,636,619,143,641,136,634,147,616,645,140,638,617,145,643,141,639,146,618,644,139,637,661,662,664,663,391,169,313,306,323,324,170,389,314,304,322,171,390,315,305,326,387,168,312,309,388,327,166,310,307,386,325,167,311,308,382,175,329,319,301,176,330,320,380,302,177,328,321,381,303,332,174,318,385,300,172,333,316,383,298,331,173,317,384,299,682,681,684,683,18,554,339,561,9,7,552,16,337,562,8,553,17,338,563,5,21,557,335,560,19,6,555,336,558,20,4,556,334,559,13,658,657,656,659,551,1,343,14,567,654,653,652,15,655,3,550,341,12,566,548,0,342,10,564,2,549,340,11,565,693,694,696,695,30,123,84,494,114,112,121,28,82,495,113,122,29,83,496,117,33,119,87,497,31,115,120,85,498,32,116,118,86,499,25,129,109,90,492,127,110,88,26,493,128,111,89,27,491,108,125,93,24,488,126,106,91,22,489,107,124,92,23,490,666,665,668,667,398,215,194,182,205,206,216,399,195,183,207,214,400,193,181,204,401,218,190,178,402,202,219,191,179,403,203,217,192,180,396,221,211,200,188,222,212,201,397,189,220,213,199,395,187,210,224,196,392,184,225,208,197,393,185,209,223,198,394,186,674,673,676,675 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#3d4915088e45e024e7bce9a29cd7ec921add83e4b04ab0fb3d527eb1a5f02fc2, 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 16:44:25 · history