Equation 677 Database

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Magma 631f10616c32…

magma 631f10616c32
Size
705
Isomorphism class hash
631f10616c3267f534cf2d03640f32f5bef3b78b25088f67aa0d7ca979c13936
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 18:21:35
Display reorder
660,7,13,404,293,285,8,14,405,294,286,6,12,406,295,284,16,10,403,296,281,11,17,401,297,282,15,9,402,298,283,410,5,19,299,291,411,3,20,300,292,412,4,18,301,290,0,409,22,302,287,2,407,23,303,288,1,408,21,304,289,662,672,661,663,524,137,452,416,191,525,138,453,417,189,526,136,454,418,190,133,523,451,415,187,521,134,449,413,188,135,522,450,414,186,458,530,128,422,197,459,531,129,423,195,460,532,127,424,196,529,457,131,421,193,527,455,132,419,194,528,456,130,420,192,686,685,688,690,219,328,464,247,235,220,326,465,245,233,218,327,466,246,234,324,215,463,250,238,216,325,461,248,236,323,217,462,249,237,470,210,319,253,241,471,211,317,251,239,472,209,318,252,240,213,469,322,256,244,214,467,320,254,242,212,468,321,255,243,668,669,664,665,356,91,200,392,145,357,92,198,393,146,358,90,199,394,144,94,355,203,391,148,353,95,201,389,149,93,354,202,390,147,208,362,89,398,143,204,363,87,399,139,616,364,88,400,617,361,207,85,397,142,359,205,86,395,140,360,206,84,396,141,676,680,681,674,631,153,559,512,25,632,154,560,513,26,633,155,561,514,24,152,630,558,511,28,628,150,556,509,29,151,629,557,510,27,565,637,159,518,31,566,638,160,519,32,567,639,161,520,30,636,564,158,517,34,634,562,156,515,35,635,563,157,516,33,666,670,667,671,595,227,428,309,500,596,228,429,310,501,597,229,430,308,502,230,594,427,305,499,592,231,425,306,497,232,593,426,307,498,434,601,225,315,506,435,602,226,316,507,436,603,224,314,508,600,433,221,311,505,598,431,222,312,503,599,432,223,313,504,699,700,694,698,111,107,545,117,621,112,105,546,118,622,113,106,547,119,623,103,110,548,120,620,108,104,549,121,618,102,109,550,122,619,551,555,98,123,627,655,652,96,653,654,656,657,97,658,659,116,552,101,126,626,114,553,99,124,624,115,554,100,125,625,703,704,702,701,168,44,367,536,476,169,42,365,537,477,170,43,366,538,478,47,171,370,535,475,172,45,368,533,473,46,173,369,534,474,373,166,39,542,482,371,167,40,543,483,372,165,41,544,484,162,376,38,541,481,163,374,36,539,479,164,375,37,540,480,697,695,693,696,350,75,607,571,274,351,76,608,572,272,352,77,609,573,273,74,349,606,570,270,347,72,604,568,271,73,348,605,569,269,613,341,81,577,280,614,342,82,578,278,615,343,83,579,279,344,612,80,576,276,345,610,78,574,277,346,611,79,575,275,677,673,679,684,446,180,57,380,643,447,181,58,381,644,448,182,59,382,645,183,445,56,379,642,443,184,54,377,640,185,444,55,378,641,48,437,178,386,649,49,438,179,387,650,50,439,177,388,651,440,51,174,385,648,441,52,175,383,646,442,53,176,384,647,675,683,678,682,71,266,488,337,583,69,267,489,335,584,70,268,490,336,585,265,67,487,340,582,68,263,485,338,580,264,66,486,339,581,494,62,257,332,589,495,60,258,333,590,496,61,259,334,591,65,493,260,331,588,63,491,261,329,586,64,492,262,330,587,687,692,689,691 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#7bddf6e5b82b5432712e2579d3d5db84306ca98ed650c79ff87e357573a5998e, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 18:21:36 · history