Equation 677 Database

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Magma 4f3666e193d9…

magma 4f3666e193d9
Size
705
Isomorphism class hash
4f3666e193d91731168059c842c7d7421ae71051958a30290c051f02c1f91632
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 21:16:09
Display reorder
660,269,197,183,214,566,267,567,195,184,215,196,565,268,185,213,265,193,562,182,210,266,194,563,180,211,264,192,564,181,212,275,203,572,189,205,273,201,573,190,206,274,202,571,191,204,199,271,568,188,208,200,272,569,186,209,198,270,570,187,207,667,662,672,669,46,99,140,33,164,47,162,100,138,34,101,163,45,139,35,42,98,167,143,32,43,96,165,141,30,44,97,166,142,31,37,105,159,135,24,38,106,160,136,25,36,107,161,137,26,104,40,158,134,27,102,41,156,132,28,103,39,157,133,29,685,687,689,690,11,315,237,542,458,9,459,316,238,543,317,457,10,239,541,7,314,454,236,538,8,312,455,234,539,6,313,456,235,540,2,321,464,228,548,1,322,465,229,549,0,323,463,230,547,320,5,460,231,544,318,3,461,232,545,319,4,462,233,546,671,668,666,664,59,446,506,13,111,57,112,447,507,14,445,113,58,505,12,55,442,110,502,16,56,443,108,503,17,54,444,109,504,15,50,452,117,512,19,48,453,118,513,20,49,451,119,511,18,448,53,116,508,22,449,51,114,509,23,450,52,115,510,21,680,682,677,673,61,578,386,410,482,62,483,579,387,411,577,481,60,385,409,64,574,478,382,406,65,575,479,383,407,63,576,480,384,408,67,584,488,392,416,68,585,489,393,417,66,583,487,391,415,580,70,484,388,412,581,71,485,389,413,582,69,486,390,414,661,663,670,665,122,494,434,554,217,120,218,495,435,555,493,216,121,433,553,125,490,220,430,550,123,491,221,431,551,124,492,219,432,552,128,500,223,440,560,126,501,224,441,561,127,499,222,439,559,496,131,226,436,556,497,129,227,437,557,498,130,225,438,558,694,696,695,693,365,599,381,364,598,366,635,634,632,633,600,601,367,380,363,368,602,603,377,360,369,604,605,378,361,370,607,606,379,362,371,654,655,653,652,372,659,658,657,656,373,650,651,649,648,638,374,639,637,636,643,375,642,641,640,647,376,646,645,644,701,702,703,704,77,289,616,617,287,75,285,290,619,618,288,286,76,614,615,73,292,283,608,609,74,293,284,611,610,72,291,282,613,612,83,295,278,629,628,81,296,276,631,630,82,294,277,626,627,298,79,281,620,621,299,80,279,623,622,297,78,280,625,624,699,700,697,698,353,174,259,518,590,351,591,175,260,519,176,589,352,258,517,349,177,586,262,514,350,178,587,263,515,348,179,588,261,516,359,172,596,257,524,357,173,597,255,525,358,171,595,256,523,168,355,592,253,520,169,356,593,254,521,170,354,594,252,522,679,681,676,684,149,422,88,398,308,147,306,423,89,399,421,307,148,87,397,145,418,311,84,394,146,419,309,85,395,144,420,310,86,396,155,428,303,94,404,153,429,304,95,405,154,427,305,93,403,424,151,302,90,400,425,152,300,91,401,426,150,301,92,402,678,674,675,683,249,324,530,341,470,250,471,325,531,339,326,469,251,529,340,248,327,466,526,337,246,328,467,527,338,247,329,468,528,336,240,330,476,536,347,241,331,477,537,345,242,332,475,535,346,333,243,472,532,343,334,244,473,533,344,335,245,474,534,342,686,688,691,692 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#e1d7ea9e4f81623cd84c542145d634570787dd3fe7cd09a50189ca2a47386599, 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 21:16:10 · history