Equation 677 Database

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Magma c59e916f178e…

magma c59e916f178e
Size
705
Isomorphism class hash
c59e916f178e2e393b540c5ec299a791746091705f2717b2ff23ad6cd8eb0eb3
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 16:47:08
Display reorder
704,86,85,84,88,89,87,91,92,90,94,95,93,614,615,617,616,613,612,620,621,622,623,618,619,627,626,628,629,625,624,633,632,635,634,631,630,637,636,639,638,641,640,642,643,644,645,647,646,648,649,651,650,653,652,654,655,657,656,659,658,677,676,687,686,196,195,197,194,192,193,201,202,203,200,198,199,439,438,440,441,442,443,436,437,432,433,434,435,421,420,423,422,425,424,426,427,429,428,431,430,462,463,465,464,467,466,461,460,457,456,459,458,444,445,446,447,448,449,451,450,453,452,455,454,690,691,698,699,62,61,60,64,65,63,67,68,66,70,71,69,359,358,355,354,357,356,350,351,352,353,348,349,370,371,367,366,368,369,362,363,364,365,361,360,335,334,330,331,333,332,327,326,329,328,325,324,346,347,342,343,344,345,338,339,340,341,336,337,667,666,672,673,22,21,23,20,18,19,12,13,14,15,16,17,120,101,99,121,100,122,97,123,98,124,96,125,107,126,105,127,106,128,103,129,104,130,102,131,133,111,134,112,132,113,136,110,137,108,135,109,139,117,140,118,138,119,142,116,143,114,141,115,680,681,684,685,45,47,46,43,44,42,38,36,37,41,39,40,266,299,297,264,298,265,295,269,296,267,294,268,290,272,288,270,289,271,293,275,291,273,292,274,278,311,276,309,277,310,281,307,279,308,280,306,284,302,282,300,283,301,287,305,285,303,286,304,695,694,700,701,320,319,322,323,318,321,312,313,314,315,316,317,246,217,218,247,216,248,220,249,221,250,219,251,223,244,224,245,222,243,226,240,227,241,225,242,205,228,206,229,204,230,208,231,209,232,207,233,211,234,212,235,210,236,214,237,215,238,213,239,693,692,702,703,83,82,81,78,79,80,73,74,72,76,77,75,484,485,480,481,482,483,490,491,486,487,488,489,474,475,476,477,478,479,472,473,468,469,470,471,508,509,505,504,506,507,514,515,511,510,512,513,499,498,501,500,502,503,496,497,492,493,494,495,660,661,663,662,48,50,49,53,51,52,56,54,55,59,57,58,556,557,552,553,554,555,563,562,558,559,560,561,547,546,549,548,551,550,544,545,540,541,542,543,516,517,518,519,520,521,523,522,525,524,526,527,529,528,530,531,532,533,535,534,536,537,538,539,678,679,682,683,11,10,9,6,7,8,0,2,1,4,5,3,156,181,182,157,180,158,184,159,185,160,183,161,187,162,188,163,186,164,190,165,191,166,189,167,169,153,170,154,168,155,172,152,173,150,171,151,175,144,176,145,174,146,178,147,179,148,177,149,689,688,697,696,262,261,263,260,258,259,252,253,254,255,256,257,599,598,595,594,597,596,590,591,592,593,588,589,610,611,607,606,608,609,602,603,604,605,601,600,575,574,570,571,572,573,567,566,569,568,565,564,587,586,582,583,584,585,579,578,581,580,576,577,668,669,671,670,27,29,28,25,26,24,35,33,34,31,32,30,377,376,380,381,372,373,389,388,393,392,384,385,401,400,405,404,397,396,413,412,417,416,408,409,378,379,383,382,375,374,391,390,394,395,387,386,403,402,407,406,399,398,414,415,418,419,411,410,665,664,674,675 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {64} 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 16:47:09 · history