Equation 677 Database

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Magma ecf56b58a4d3…

magma ecf56b58a4d3
Size
705
Isomorphism class hash
ecf56b58a4d349a96e16f864cc0f7b028110c0950fa1b8ac8ae676f10431141c
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 20:43:54
Display reorder
660,81,407,207,125,133,76,205,126,134,408,78,409,206,124,135,203,73,406,128,132,75,204,404,129,130,71,202,405,127,131,93,213,413,123,139,121,88,211,414,140,91,212,415,122,141,209,85,412,119,138,210,87,410,120,136,208,82,411,118,137,662,665,663,667,61,278,342,357,441,62,340,355,442,279,63,277,341,356,443,345,60,274,353,440,58,343,275,354,438,59,344,276,352,439,67,337,284,348,447,346,68,338,285,448,69,339,283,347,449,336,66,280,351,446,334,64,281,349,444,335,65,282,350,445,686,691,685,688,116,18,52,234,163,117,53,232,164,19,115,20,54,233,165,55,112,21,237,162,113,56,22,235,160,114,57,23,236,161,107,50,16,229,154,230,108,51,17,155,106,49,15,231,156,46,110,12,228,157,47,111,13,226,158,48,109,14,227,159,668,669,671,670,360,523,291,465,559,358,289,466,560,524,359,525,290,467,561,287,363,522,464,558,361,288,520,462,556,362,286,521,463,557,366,297,529,471,565,472,364,295,530,566,365,296,531,473,567,293,369,528,470,564,294,367,526,468,562,292,368,527,469,563,678,674,676,673,74,299,499,535,373,70,500,536,374,300,72,298,501,537,375,498,80,302,534,372,77,496,303,532,370,79,497,301,533,371,86,505,305,541,379,542,83,506,306,380,84,507,304,543,381,504,92,308,540,378,502,89,309,538,376,503,90,307,539,377,661,666,672,664,146,453,583,631,223,147,584,632,224,454,145,455,585,633,225,582,142,452,630,222,143,580,450,628,220,144,581,451,629,221,152,589,459,637,214,638,153,590,460,215,151,591,461,639,216,588,148,458,636,217,586,149,456,634,218,587,150,457,635,219,694,700,696,698,389,30,431,486,397,390,432,487,398,28,388,29,433,488,399,430,392,26,489,396,393,428,27,490,394,391,429,25,491,395,387,437,24,492,403,655,385,654,653,652,386,658,657,659,656,436,383,32,493,402,434,384,33,494,400,435,382,31,495,401,702,704,701,703,316,419,40,607,477,317,41,608,478,420,318,421,42,609,479,43,319,418,606,476,320,44,416,604,474,321,45,417,605,475,314,38,425,613,483,614,315,39,426,484,313,37,427,615,485,34,310,424,612,482,35,311,422,610,480,36,312,423,611,481,697,699,695,693,197,595,260,264,571,198,261,262,572,596,196,597,259,263,573,256,200,594,267,570,201,257,592,265,568,199,258,593,266,569,195,251,601,270,577,268,193,252,602,578,194,250,603,269,579,254,191,600,273,576,255,192,598,271,574,253,190,599,272,575,679,682,681,684,333,6,547,643,511,331,548,644,512,7,332,8,549,645,513,546,329,9,642,510,330,544,10,640,508,328,545,11,641,509,324,553,4,649,517,650,322,554,5,518,323,555,3,651,519,552,327,1,648,516,550,325,0,646,514,551,326,2,647,515,675,683,680,677,99,619,242,177,183,97,243,175,181,620,98,621,241,176,182,238,95,618,173,179,96,239,616,174,180,94,240,617,172,178,105,248,625,168,189,166,103,249,626,187,104,247,627,167,188,244,101,624,171,185,245,102,622,169,186,246,100,623,170,184,692,689,690,687 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#cd941b7de786c28317b7a103413c14ee77b5f1d3c398e3760811607e92439ad2, 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 20:43:55 · history