Equation 677 Database

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Magma 54799bb8b128…

magma 54799bb8b128
Size
705
Isomorphism class hash
54799bb8b128e594dafddc85dee62e457d195ff55d160c35729867fa4ede013c
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 16:55:05
Display reorder
660,157,473,145,133,169,158,134,471,146,170,472,132,156,144,168,153,469,141,129,165,154,470,142,130,166,155,468,143,131,167,151,464,163,139,175,152,462,164,140,176,150,463,162,138,174,467,147,159,135,171,465,148,160,136,172,466,149,161,137,173,685,686,688,687,290,500,283,263,260,288,261,498,284,258,499,262,289,282,259,286,503,279,266,256,287,501,280,264,257,285,502,281,265,255,274,506,296,269,251,275,504,294,267,249,273,505,295,268,250,509,277,292,272,254,507,278,293,270,252,508,276,291,271,253,701,702,704,703,461,106,447,428,588,459,426,107,448,586,105,427,460,449,587,457,109,446,431,591,458,110,444,429,589,456,108,445,430,590,438,112,452,434,583,439,113,450,432,584,440,111,451,433,585,115,441,455,437,582,116,442,453,435,580,114,443,454,436,581,670,669,672,671,318,43,306,518,330,319,516,44,307,331,42,517,320,308,332,317,46,305,521,329,315,47,303,519,327,316,45,304,520,328,297,41,309,513,321,298,39,310,514,322,299,40,311,515,323,37,300,312,512,324,38,301,313,510,325,36,302,314,511,326,680,677,679,678,529,344,124,26,70,530,24,342,125,71,343,25,528,123,69,532,340,127,29,66,533,341,128,27,67,531,339,126,28,68,122,335,527,32,61,120,333,525,30,62,121,334,526,31,60,338,118,523,35,64,336,119,524,33,65,337,117,522,34,63,689,690,691,692,403,88,382,380,566,404,378,89,383,564,87,379,402,381,565,399,84,385,376,569,400,85,386,377,567,401,86,384,375,568,388,94,394,371,561,389,95,395,369,562,387,93,393,370,563,90,391,397,374,560,91,392,398,372,558,92,390,396,373,559,697,698,700,699,614,593,651,629,619,615,630,594,649,620,592,628,613,650,621,610,596,647,632,618,611,597,648,633,616,612,595,646,631,617,642,599,605,635,625,640,600,606,636,626,641,598,604,634,627,602,645,608,638,624,603,643,609,639,622,601,644,607,637,623,661,662,664,663,186,479,222,203,200,187,201,477,223,198,478,202,188,224,199,185,475,221,206,196,183,476,219,204,197,184,474,220,205,195,213,485,177,209,191,214,483,178,207,189,215,484,179,208,190,481,216,180,212,194,482,217,181,210,192,480,218,182,211,193,682,681,684,683,424,51,104,576,407,425,574,52,102,405,53,575,423,103,406,420,50,100,579,410,421,48,101,577,408,422,49,99,578,409,657,57,658,659,656,415,58,416,573,411,652,59,653,654,655,56,98,418,572,414,54,96,419,570,412,55,97,417,571,413,693,694,696,695,548,72,540,359,351,546,357,73,541,352,74,358,547,542,353,551,75,543,362,354,549,76,544,360,355,550,77,545,361,356,538,78,554,365,349,539,79,552,363,350,537,80,553,364,348,81,534,557,368,345,82,535,555,366,346,83,536,556,367,347,666,665,668,667,234,19,494,7,246,235,8,20,492,247,18,6,236,493,248,233,22,497,10,245,231,23,495,11,243,232,21,496,9,244,489,17,225,5,237,490,15,226,3,238,491,16,227,4,239,13,488,228,0,240,14,486,229,2,241,12,487,230,1,242,674,673,676,675 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#48d4131c324a99301720abcc6dab4afc68cf81d40922963883b47bf0604d0986, 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 16:55:07 · history