Equation 677 Database

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Magma eed91bc51209…

magma eed91bc51209
Size
705
Isomorphism class hash
eed91bc5120930c0d7cbe4ff452c24bc313d7678182060b5e62937728dec918c
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 15:58:48
Display reorder
660,84,231,344,336,238,345,229,85,334,239,86,343,335,240,230,234,87,340,339,237,232,88,341,337,235,233,89,342,338,236,226,90,331,350,244,227,91,332,351,245,228,92,333,349,246,346,93,225,330,243,94,223,328,347,241,95,224,329,348,242,685,686,688,687,13,406,426,422,68,424,407,14,423,66,12,425,421,67,408,409,16,429,418,71,410,17,427,419,69,411,15,428,420,70,404,19,413,432,63,405,20,414,430,64,403,18,412,431,65,435,22,400,416,62,23,401,417,433,60,21,402,415,434,61,701,702,704,703,79,191,615,598,316,613,192,80,599,317,78,614,600,318,190,187,82,611,601,319,188,83,612,602,320,189,81,610,603,321,197,77,596,606,322,198,75,597,604,323,196,76,595,605,324,609,73,193,592,325,74,194,593,607,326,72,195,594,608,327,670,669,672,671,204,464,442,473,457,443,465,202,474,458,203,444,472,459,463,460,200,445,476,456,461,201,446,477,454,462,199,447,475,455,470,210,479,440,448,471,208,480,441,449,469,209,478,439,450,436,206,466,482,451,207,467,483,437,452,205,468,481,438,453,680,677,679,678,215,517,492,141,501,490,518,216,142,499,214,491,143,500,519,516,211,495,140,497,514,212,493,138,498,515,213,494,139,496,508,221,132,487,507,509,222,133,488,505,510,220,134,489,506,486,217,511,135,503,218,512,136,484,504,219,513,137,485,502,689,690,691,692,285,164,10,171,574,11,162,283,172,575,284,9,173,576,163,167,288,6,170,577,165,286,7,168,578,166,287,8,169,579,159,291,177,0,572,160,289,178,2,573,161,290,179,1,571,4,294,158,176,568,292,156,174,5,569,293,157,175,3,570,697,698,700,699,107,119,639,622,130,637,117,105,623,131,106,638,624,129,118,115,103,635,625,126,116,104,636,626,127,114,102,634,627,128,110,98,620,630,121,108,96,621,628,122,109,97,619,629,120,633,101,113,616,124,99,111,617,631,125,100,112,618,632,123,661,662,664,663,24,40,359,255,366,360,41,25,253,364,26,358,254,365,39,36,27,362,258,369,37,28,363,256,367,38,29,361,257,368,46,30,250,357,372,47,31,251,355,370,45,32,252,356,371,353,33,42,249,375,34,43,247,354,373,35,44,248,352,374,682,681,684,683,587,314,182,300,305,183,312,588,298,303,586,181,299,304,313,310,590,185,296,308,311,591,186,297,306,309,589,184,295,307,647,585,644,645,646,315,583,301,180,302,642,584,640,641,643,657,581,659,656,658,582,651,649,648,650,580,655,652,653,654,693,694,696,695,148,558,532,524,548,533,556,149,525,549,147,534,523,547,557,561,144,535,520,544,559,145,536,521,545,560,146,537,522,546,564,154,530,538,554,562,155,531,539,555,563,153,529,540,553,541,150,567,526,550,151,565,527,542,551,152,566,528,543,552,666,665,668,667,59,282,391,384,270,392,280,57,382,268,58,393,383,269,281,278,55,390,387,266,279,56,388,385,267,277,54,389,386,265,273,50,379,397,261,271,48,380,398,259,272,49,381,399,260,396,53,276,378,264,51,274,376,394,262,52,275,377,395,263,674,673,676,675 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#2ab683a2f54af56adf82381d164449f2b2adaada784a6acf8eff870c9ce46309, 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 15:58:50 · history