Equation 677 Database

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Magma 8ec57b651e02…

magma 8ec57b651e02
Size
705
Isomorphism class hash
8ec57b651e02cbc63af8bb3dc9a05691e7f9eb4ac864d621cc7a36fb504e56e1
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 21:23:35
Display reorder
660,347,145,528,480,384,348,143,526,478,382,346,144,479,527,383,350,148,531,483,387,351,146,529,481,385,349,147,530,482,386,151,353,534,486,390,149,354,532,484,388,150,352,533,485,389,356,154,537,489,393,357,152,535,487,391,355,153,536,488,392,672,668,663,666,258,225,169,164,43,256,223,167,165,41,257,224,166,168,42,261,221,172,163,46,259,222,170,161,44,260,220,171,162,45,216,253,175,155,38,214,254,173,156,39,215,255,174,157,40,252,219,178,158,37,250,217,176,159,35,251,218,177,160,36,689,685,686,687,516,296,20,77,101,514,297,21,78,102,515,295,79,22,103,519,292,19,80,104,517,293,17,81,105,518,294,18,82,106,287,522,11,75,99,288,520,12,76,100,286,521,13,74,98,525,290,14,71,95,523,291,15,72,96,524,289,16,73,97,667,669,670,665,396,189,468,227,432,394,190,466,228,430,395,188,226,467,431,399,185,471,230,435,397,186,469,231,433,398,187,470,229,434,180,402,474,233,438,181,400,472,234,436,179,401,473,232,437,405,183,477,236,441,403,184,475,237,439,404,182,476,235,440,674,679,676,673,408,57,372,364,245,406,58,370,365,246,407,56,366,371,244,411,53,375,367,248,409,54,373,368,249,410,55,374,369,247,48,414,378,362,243,49,412,376,363,241,47,413,377,361,242,417,51,381,358,239,415,52,379,359,240,416,50,380,360,238,664,661,671,662,552,281,141,130,504,550,282,142,128,502,551,280,129,140,503,555,284,137,126,507,553,285,138,127,505,554,283,139,125,506,279,558,132,121,510,277,556,133,119,508,278,557,131,120,509,561,275,135,124,513,559,276,136,122,511,560,274,134,123,512,697,693,696,694,621,93,620,623,622,615,94,614,613,612,617,92,619,616,618,633,89,632,635,634,624,90,625,627,626,628,91,629,631,630,84,645,644,647,646,85,636,637,639,638,83,641,640,643,642,657,87,656,659,658,648,88,649,651,650,653,86,652,655,654,703,701,702,704,6,61,444,588,201,7,59,442,586,199,5,60,587,443,200,9,64,447,591,197,10,62,445,589,198,8,63,446,590,196,67,4,450,594,195,65,2,448,592,193,66,3,449,593,194,610,70,453,597,611,0,68,451,595,192,1,69,452,596,191,699,695,700,698,344,30,492,272,600,345,31,490,273,598,343,29,271,491,599,340,33,495,268,603,341,34,493,269,601,342,32,494,270,602,28,335,498,263,606,26,336,496,264,604,27,334,497,262,605,338,24,501,266,609,339,25,499,267,607,337,23,500,265,608,681,680,684,677,576,207,456,540,420,574,205,454,538,418,575,206,539,455,419,579,203,459,543,423,577,204,457,541,421,578,202,458,542,422,213,582,462,546,426,211,580,460,544,424,212,581,461,545,425,585,209,465,549,429,583,210,463,547,427,584,208,464,548,428,683,678,675,682,306,112,326,310,564,304,110,327,311,562,305,111,312,325,563,309,108,322,313,567,307,109,323,314,565,308,107,324,315,566,118,301,332,316,570,116,302,333,317,568,117,303,331,318,569,300,114,328,319,573,298,115,329,320,571,299,113,330,321,572,690,692,688,691 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#edd749230bc58665165cb5ff86cf593765d0cefcd490b689f1cd7ce77c95b856, 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 21:23:35 · history