Equation 677 Database

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Magma 84d790dd3e5f…

magma 84d790dd3e5f
Size
705
Isomorphism class hash
84d790dd3e5f190cb4144d785be84c4ffbb1155c15d50eaa17d1eb8c6846761f
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 15:07:41
Display reorder
660,617,358,584,609,596,618,359,585,607,597,616,583,608,595,357,361,620,580,605,592,362,621,581,606,593,360,619,582,604,594,623,364,590,615,602,624,365,591,613,603,622,363,589,614,601,611,367,626,586,598,368,627,587,612,599,366,625,588,610,600,687,688,686,685,253,443,257,232,223,251,441,258,230,221,252,259,231,222,442,446,249,256,235,219,444,250,254,233,220,445,248,255,234,218,244,449,263,238,229,242,447,264,236,227,243,448,265,237,228,241,452,247,262,225,450,245,260,239,226,451,246,261,240,224,703,704,701,702,568,352,536,561,548,569,353,537,559,549,570,535,560,547,351,355,571,532,557,544,356,572,533,558,545,354,573,534,556,546,574,350,542,567,554,575,348,543,565,555,576,349,541,566,553,563,346,577,538,550,347,578,539,564,551,345,579,540,562,552,671,672,670,669,2,76,461,167,266,1,77,459,168,267,0,460,166,268,78,75,5,464,163,269,73,3,462,164,270,74,4,463,165,271,8,67,456,173,272,6,68,457,174,273,7,69,458,172,274,169,70,11,455,275,71,9,453,170,276,72,10,454,171,277,679,680,678,677,278,90,293,472,311,279,88,294,473,312,280,295,471,313,89,86,281,292,475,310,87,282,290,476,308,85,283,291,474,309,284,81,299,470,302,285,79,300,468,303,286,80,301,469,304,466,84,287,298,305,82,288,296,467,306,83,289,297,465,307,692,691,690,689,334,194,101,59,519,332,195,102,57,520,333,100,58,521,193,197,337,97,55,522,198,335,98,56,523,196,336,99,54,524,329,192,92,50,517,330,190,93,48,518,331,191,91,49,516,53,188,328,95,513,189,326,96,51,514,187,327,94,52,515,699,700,698,697,31,21,123,144,138,32,22,121,142,136,30,122,143,137,23,20,34,126,140,134,18,35,124,141,135,19,33,125,139,133,29,12,118,150,129,27,13,119,148,127,28,14,120,149,128,146,15,25,117,132,16,26,115,147,130,17,24,116,145,131,663,664,662,661,369,630,385,407,398,370,628,386,405,396,371,384,406,397,629,633,372,381,410,394,631,373,382,408,395,632,374,383,409,393,375,636,391,413,404,376,634,392,411,402,377,635,390,412,403,416,639,378,387,400,637,379,388,414,401,638,380,389,415,399,682,683,684,681,654,103,652,655,653,658,104,656,659,657,650,648,651,649,105,106,199,344,531,60,107,641,640,642,643,108,646,645,647,644,204,109,343,529,61,205,110,341,530,62,203,111,342,528,63,525,112,200,339,64,113,201,340,526,65,114,202,338,527,66,695,696,693,694,505,318,181,489,483,506,319,182,490,484,504,183,491,485,317,314,501,184,492,486,315,502,185,493,487,316,503,186,494,488,511,324,179,495,481,512,325,180,496,482,510,323,178,497,480,498,320,507,175,477,321,508,176,499,478,322,509,177,500,479,667,668,665,666,423,43,429,156,216,424,44,430,154,217,425,431,155,215,42,46,426,432,152,212,47,427,433,153,213,45,428,434,151,214,421,41,435,162,207,422,39,436,160,208,420,40,437,161,206,158,37,417,438,210,38,418,439,159,211,36,419,440,157,209,675,676,673,674 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#055eb219830141adc126b0e3c095dec26895b5c9338d223a671ccb522fe00e95, 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 15:07:42 · history