Equation 677 Database

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Magma 690295f10e29…

magma 690295f10e29
Size
705
Isomorphism class hash
690295f10e29e49a01804344cd84644b026c768ee88af9f3719c322d2c6adcb4
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 19:53:19
Display reorder
660,110,33,361,351,144,108,34,142,362,352,109,35,143,360,353,113,32,140,357,354,111,30,141,358,355,112,31,139,359,356,105,39,150,367,349,106,40,148,368,350,366,107,41,149,348,38,104,146,363,345,36,102,147,364,346,37,103,145,365,347,685,686,688,687,400,406,439,428,14,401,407,12,440,426,399,405,13,438,427,403,409,17,435,424,404,410,15,436,425,402,408,16,437,423,398,412,9,430,419,396,413,10,431,417,429,397,411,11,418,415,394,8,433,422,416,395,6,434,420,414,393,7,432,421,701,702,704,703,333,137,571,562,245,334,138,243,572,563,335,136,244,573,564,336,133,248,570,565,337,134,246,568,566,338,135,247,569,567,339,128,240,577,560,340,129,241,578,561,579,341,127,242,559,131,342,239,576,556,132,343,237,574,557,130,344,238,575,558,670,669,672,671,457,468,445,479,25,458,469,26,446,477,456,470,24,444,478,453,467,28,441,482,454,465,29,442,480,455,466,27,443,481,463,474,23,451,485,464,475,21,452,483,450,462,476,22,484,473,459,19,447,488,471,460,20,448,486,472,461,18,449,487,680,677,679,678,496,502,93,523,258,497,503,259,94,524,495,501,260,95,522,499,505,257,92,519,500,506,255,90,520,498,504,256,91,521,494,508,249,99,514,492,509,250,100,515,101,493,507,251,513,511,490,252,98,517,512,491,253,96,518,510,489,254,97,516,689,690,691,692,72,81,310,545,215,73,82,216,311,543,74,83,214,309,544,75,80,211,313,548,76,78,212,314,546,77,79,213,312,547,70,87,221,316,540,71,88,222,317,541,315,69,89,220,542,86,66,217,319,539,84,67,218,320,537,85,68,219,318,538,697,698,700,699,602,605,639,627,581,603,606,582,637,625,601,604,580,638,626,598,608,584,635,623,599,609,585,636,624,600,607,583,634,622,593,611,587,630,618,594,612,588,628,616,629,592,610,586,617,614,596,590,633,621,615,597,591,631,619,613,595,589,632,620,661,662,664,663,49,122,376,54,161,50,120,162,377,55,48,121,160,375,56,52,125,157,379,57,53,123,158,380,58,51,124,159,378,59,47,117,152,374,60,45,118,153,372,61,373,46,119,151,62,116,43,155,370,63,114,44,156,371,64,115,42,154,369,65,682,681,684,683,4,232,552,225,326,5,233,324,550,223,3,231,325,551,224,1,235,322,555,228,0,236,323,553,226,2,234,321,554,227,645,646,332,647,644,230,126,330,549,229,642,640,641,331,643,656,657,328,659,658,648,649,329,651,650,652,653,327,655,654,693,694,696,695,288,297,278,266,527,289,298,525,276,264,290,299,526,277,265,287,300,530,274,262,285,301,528,275,263,286,302,529,273,261,294,303,533,284,272,295,304,531,282,270,283,296,305,532,271,306,293,536,280,268,307,291,534,281,269,308,292,535,279,267,666,665,668,667,190,201,179,167,384,191,199,385,180,168,192,200,386,178,166,189,204,383,175,163,187,202,381,176,164,188,203,382,177,165,196,207,390,185,173,197,205,391,186,174,184,198,206,392,172,210,195,389,181,169,208,193,387,182,170,209,194,388,183,171,674,673,676,675 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#b307f9e79abd0b0dc3c5454ee1dbc0a12bcd3b395b4c4aa55143605b1deda3bc, 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 19:53:20 · history