Equation 677 Database

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Magma 790d7f18198d…

magma 790d7f18198d
Size
705
Isomorphism class hash
790d7f18198d3d9b39dff66ee7f8d3d869aa08327081d9549464dbfc8edee12e
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 16:22:29
Display reorder
660,217,327,340,362,368,218,366,328,341,360,216,367,329,339,361,330,220,364,343,358,331,221,365,344,359,219,332,363,342,357,223,333,374,346,353,224,334,372,347,351,222,335,373,345,352,336,226,370,349,356,350,337,227,371,354,338,225,369,348,355,685,686,688,687,123,438,6,22,431,124,429,439,7,23,125,430,440,8,21,437,122,434,9,18,435,120,432,10,19,121,436,433,11,20,129,444,426,4,13,130,445,427,5,14,131,446,428,3,12,443,128,425,1,16,0,441,126,423,17,442,127,424,2,15,701,702,704,703,322,585,599,559,565,323,566,586,597,560,321,564,587,598,558,584,325,568,595,562,582,326,569,596,563,324,583,567,594,561,320,576,571,590,557,318,577,572,588,555,319,578,570,589,556,579,316,574,593,553,591,580,317,575,554,581,315,573,592,552,670,669,672,671,448,153,165,178,133,449,134,154,166,179,447,132,155,167,177,152,451,136,164,174,150,452,137,162,175,450,151,135,163,176,454,144,139,156,169,455,145,140,157,170,453,146,138,158,168,147,457,142,159,172,160,148,458,143,173,149,456,141,161,171,680,677,679,678,89,186,465,481,27,87,28,187,466,482,88,29,188,467,480,189,85,26,468,477,190,86,24,469,478,84,191,25,470,479,95,184,33,463,472,93,185,34,464,473,94,183,35,462,471,180,91,32,459,475,460,181,92,30,476,182,90,31,461,474,689,690,691,692,210,270,286,539,56,211,54,271,287,537,212,55,272,285,538,273,213,59,282,542,274,214,57,283,540,215,275,58,284,541,208,268,51,277,534,209,269,52,278,535,207,267,53,276,536,264,204,50,280,533,281,265,205,48,531,266,206,49,279,532,697,698,700,699,83,633,647,607,613,81,614,634,645,608,82,612,635,646,606,632,79,616,643,610,630,80,617,644,611,78,631,615,642,609,74,624,619,638,605,72,625,620,636,603,73,626,618,637,604,627,77,622,641,601,639,628,75,623,602,629,76,621,640,600,661,662,664,663,104,238,244,382,389,102,387,239,245,383,103,388,237,243,381,234,107,392,240,385,235,105,390,241,386,106,236,391,242,384,99,229,395,250,380,100,230,393,251,378,101,228,394,249,379,232,98,398,246,376,247,233,96,396,377,231,97,397,248,375,682,681,684,683,66,288,548,302,306,67,307,289,546,300,68,308,290,547,301,291,69,305,551,298,292,70,303,549,299,71,293,304,550,297,64,652,654,655,653,65,657,658,659,656,63,649,648,650,651,312,60,311,545,296,543,313,61,309,294,314,62,310,544,295,693,694,696,695,195,484,505,512,521,196,519,485,506,510,197,520,483,504,511,487,194,524,501,508,488,192,522,502,509,193,486,523,503,507,201,490,527,496,518,202,491,525,497,516,203,489,526,495,517,493,200,530,499,514,500,494,198,528,515,492,199,529,498,513,666,665,668,667,117,406,412,255,37,118,38,407,413,256,119,36,405,411,257,409,116,40,415,254,410,114,41,416,252,115,408,39,414,253,108,404,43,418,261,109,402,44,419,262,110,403,42,417,263,400,111,46,421,260,422,401,112,47,258,399,113,45,420,259,674,673,676,675 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#2ec821928dae411f986b7c636eee0f3d0451d16a0e775a52641e8351195889f9, 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 16:22:31 · history