Equation 677 Database

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Magma b66db9bd82a9…

magma b66db9bd82a9
Size
705
Isomorphism class hash
b66db9bd82a98954e76a67a6d86e42794453c08b13cd30b80c9e4effb5b6d81f
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 19:15:14
Display reorder
660,164,159,371,141,178,160,142,162,369,179,143,161,163,370,177,167,158,367,140,174,368,156,165,138,175,166,157,366,139,176,150,170,377,147,184,151,168,375,148,185,152,169,376,149,183,173,153,373,146,180,171,154,374,144,181,172,155,372,145,182,685,686,688,687,476,471,221,453,440,472,454,474,219,438,455,473,475,220,439,479,470,217,452,443,218,468,477,450,441,478,469,216,451,442,462,482,212,459,446,463,480,210,460,444,464,481,211,461,445,485,465,215,458,449,483,466,213,456,447,484,467,214,457,448,701,702,704,703,364,346,575,338,98,347,336,365,573,96,337,345,363,574,97,360,342,571,341,101,572,343,361,339,99,362,344,570,340,100,352,355,566,333,93,353,356,564,334,94,351,354,565,335,95,358,348,569,332,92,359,349,567,330,90,357,350,568,331,91,670,669,672,671,245,225,29,493,255,226,494,243,27,256,492,227,244,28,257,241,224,25,496,254,26,222,242,497,252,240,223,24,495,253,231,236,20,491,246,232,234,18,489,247,233,235,19,490,248,239,230,23,487,249,237,228,21,488,250,238,229,22,486,251,680,677,679,678,269,531,111,513,504,532,514,267,112,505,515,533,268,113,506,265,530,110,512,507,108,528,266,510,508,264,529,109,511,509,522,260,102,519,502,523,258,103,520,503,524,259,104,521,501,263,525,105,518,498,261,526,106,516,499,262,527,107,517,500,689,690,691,692,71,135,306,117,554,136,118,69,307,552,119,137,70,308,553,67,134,309,116,557,310,132,68,114,555,66,133,311,115,556,126,77,312,123,549,127,75,313,124,550,128,76,314,125,551,73,129,315,122,548,74,130,316,120,546,72,131,317,121,547,697,698,700,699,623,611,635,592,584,609,593,621,633,582,591,610,622,634,583,619,607,631,588,587,632,608,620,589,585,618,606,630,590,586,602,614,626,598,579,600,612,624,599,580,601,613,625,597,581,617,605,629,594,578,615,603,627,595,576,616,604,628,596,577,661,662,664,663,425,413,195,393,384,411,394,423,196,385,395,412,424,197,386,421,409,194,392,387,192,410,422,390,388,420,408,193,391,389,404,416,186,399,382,402,414,187,400,383,403,415,188,401,381,419,407,189,398,378,417,405,190,396,379,418,406,191,397,380,682,681,684,683,321,3,79,558,326,4,559,322,80,324,560,5,323,78,325,320,2,82,561,329,83,1,318,562,327,319,0,81,563,328,641,640,85,643,642,645,644,86,647,646,636,637,84,638,639,653,652,88,655,654,656,657,89,659,658,649,648,87,651,650,693,694,696,695,294,287,536,276,63,285,277,295,534,64,278,286,296,535,65,297,283,539,279,62,537,284,298,280,60,299,282,538,281,61,293,300,542,274,54,291,301,540,275,55,292,302,541,273,56,303,289,545,270,57,304,290,543,271,58,305,288,544,272,59,666,665,668,667,11,30,209,432,36,31,433,9,207,34,434,32,10,208,35,7,37,205,435,39,206,38,8,436,40,6,41,204,437,33,42,17,200,430,45,44,15,198,431,46,47,16,199,429,43,13,48,203,426,51,14,50,201,427,52,12,53,202,428,49,674,673,676,675 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#966159413732cc97ab9cbe48ea19b17c045c0e7dae7d4f88fdd62e86aa428734, 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 19:15:15 · history