Equation 677 Database

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Magma 8dd379457b14…

magma 8dd379457b14
Size
705
Isomorphism class hash
8dd379457b1408f0041c417bf024f058f2454313ae569835ca1176c8cb0a0299
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 19:19:14
Display reorder
660,346,129,114,227,132,228,347,127,112,130,128,226,348,113,131,230,349,125,117,135,231,350,126,115,133,229,351,124,116,134,344,120,109,233,138,345,118,110,234,136,343,119,111,232,137,340,123,108,236,141,341,121,106,237,139,342,122,107,235,140,661,672,665,668,448,26,464,15,624,16,449,24,465,625,25,17,450,463,623,14,451,29,460,620,12,452,27,461,621,13,453,28,462,622,454,32,470,21,630,455,30,471,22,631,456,31,469,23,629,457,35,466,20,626,458,33,467,18,627,459,34,468,19,628,690,691,687,686,500,476,512,369,560,367,501,477,513,561,475,368,499,511,559,365,496,472,508,556,366,497,473,509,557,364,498,474,510,558,506,482,518,375,566,507,483,519,373,567,505,481,517,374,565,502,478,514,371,562,503,479,515,372,563,504,480,516,370,564,662,667,664,666,256,404,6,292,262,293,257,405,7,263,403,294,258,8,264,295,255,400,9,265,296,253,401,10,266,297,254,402,11,267,605,410,4,298,606,607,411,5,299,608,603,409,3,300,604,261,406,1,301,252,259,407,0,302,250,260,408,2,303,251,676,681,682,673,333,313,636,269,316,270,331,314,637,317,315,268,332,635,318,272,329,312,632,319,273,330,310,633,320,271,328,311,634,321,339,304,642,275,322,337,305,643,276,323,338,306,641,274,324,335,307,638,278,325,336,308,639,279,326,334,309,640,277,327,663,669,670,671,164,524,244,356,149,357,165,525,245,150,523,355,163,246,148,352,160,520,247,152,353,161,521,248,153,354,162,522,249,151,155,530,242,362,147,156,531,243,363,145,154,529,241,361,146,158,526,238,358,143,159,527,239,359,144,157,528,240,360,142,699,698,695,693,72,83,572,95,613,96,73,84,573,614,85,94,74,571,612,98,75,86,568,609,99,76,87,569,610,97,77,88,570,611,78,89,578,101,619,659,657,656,102,658,82,93,577,100,618,79,90,574,104,615,80,91,575,105,616,81,92,576,103,617,703,704,701,702,583,39,287,63,428,64,584,40,288,429,41,65,582,286,427,62,579,38,290,424,60,580,36,291,425,61,581,37,289,426,589,45,285,69,434,590,46,283,70,435,588,47,284,71,433,585,44,281,68,430,586,42,282,66,431,587,43,280,67,432,696,694,697,700,595,536,214,191,392,192,596,537,215,393,535,190,594,216,391,194,591,532,217,388,195,592,533,218,389,193,593,534,219,390,601,542,220,197,398,602,543,221,198,399,600,541,222,196,397,597,538,223,200,394,598,539,224,201,395,599,540,225,199,396,679,675,680,684,488,443,416,55,648,56,489,444,417,649,442,54,487,415,647,58,484,446,412,644,59,485,447,413,645,57,486,445,414,646,494,441,422,53,654,495,439,423,51,655,493,440,421,52,653,490,437,418,49,650,491,438,419,50,651,492,436,420,48,652,674,683,678,677,210,187,173,379,548,380,208,188,174,549,189,381,209,172,547,378,213,186,176,544,376,211,184,177,545,377,212,185,175,546,205,178,171,385,554,206,179,169,386,555,207,180,170,387,553,204,181,167,384,550,202,182,168,382,551,203,183,166,383,552,692,688,689,685 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#9c565a9fd79b154e390f38dd387d90fedf9817e0675733b83815c4693870456f, 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 19:19:15 · history