Equation 677 Database

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Magma ea632165bfdd…

magma ea632165bfdd
Size
705
Isomorphism class hash
ea632165bfdd0205d67c58e9ef9dae9fe46fce54fb341a4442627ce02a09800e
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 16:45:20
Display reorder
660,314,313,312,316,317,315,319,320,318,322,323,321,345,332,330,346,331,347,335,344,333,342,334,343,327,336,328,337,329,338,326,339,324,340,325,341,176,358,174,359,175,357,179,354,177,355,178,356,171,349,172,350,173,348,170,352,168,353,169,351,680,675,677,700,426,428,427,431,429,430,423,424,425,422,420,421,445,437,435,446,436,444,433,448,434,449,432,447,443,451,441,452,442,450,439,454,440,455,438,453,105,464,106,462,107,463,104,467,102,465,103,466,96,459,97,460,98,461,99,458,100,456,101,457,696,692,693,704,290,289,288,292,293,291,295,296,294,298,299,297,265,306,307,266,308,264,309,268,310,269,311,267,304,271,305,272,303,270,300,274,301,275,302,273,156,283,157,284,158,282,159,286,160,287,161,285,162,281,163,279,164,280,165,277,166,278,167,276,670,664,668,684,489,491,490,487,488,486,482,480,481,485,483,484,510,503,501,511,502,512,499,513,500,514,498,515,494,508,492,509,493,507,497,504,495,505,496,506,0,469,2,470,1,468,4,472,5,473,3,471,7,475,8,476,6,474,10,478,11,479,9,477,682,674,678,698,529,528,530,531,532,533,534,535,536,537,538,539,556,541,542,557,540,555,544,552,545,553,543,554,547,562,548,563,546,561,550,558,551,559,549,560,26,523,24,524,25,522,29,526,27,527,28,525,32,521,30,519,31,520,35,517,33,518,34,516,695,687,690,701,633,635,634,631,632,630,626,624,625,629,627,628,655,647,645,656,646,654,643,658,644,659,642,657,638,653,636,651,637,652,641,649,639,650,640,648,247,622,248,623,246,621,250,618,251,619,249,620,245,613,243,614,244,612,241,616,242,617,240,615,697,686,691,702,57,59,58,55,56,54,50,48,49,53,51,52,79,71,69,80,70,78,67,82,68,83,66,81,62,77,60,75,61,76,65,73,63,74,64,72,37,87,38,88,36,89,40,86,41,84,39,85,43,93,44,94,42,95,46,92,47,90,45,91,661,662,663,673,382,381,383,380,378,379,372,373,374,375,376,377,398,388,389,396,387,397,384,401,385,399,386,400,394,404,395,402,393,403,390,407,391,405,392,406,188,361,186,362,187,360,191,364,189,365,190,363,183,367,184,368,185,366,182,370,180,371,181,369,681,676,679,699,121,120,122,123,124,125,126,127,128,129,130,131,147,133,134,148,132,149,136,146,137,144,135,145,139,153,140,154,138,155,142,152,143,150,141,151,252,115,253,116,254,114,255,118,256,119,257,117,258,113,259,111,260,112,261,109,262,110,263,108,694,688,689,703,583,582,584,585,586,587,580,581,579,576,577,578,605,589,590,603,588,604,592,601,593,602,591,600,595,611,596,609,594,610,598,607,599,608,597,606,22,575,23,573,21,574,18,571,19,572,20,570,13,566,14,564,12,565,16,569,17,567,15,568,672,666,667,683,198,200,199,203,201,202,195,196,197,194,192,193,217,209,207,218,208,216,205,220,206,221,204,219,215,223,213,224,214,222,211,226,212,227,210,225,414,235,415,236,416,234,417,238,418,239,419,237,412,233,413,231,411,232,408,229,409,230,410,228,671,665,669,685 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, 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 16:45:21 · history