Equation 677 Database

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Magma bcae99432f2e…

magma bcae99432f2e
Size
705
Isomorphism class hash
bcae99432f2ed5a375ede8418d4ce546c981c9bbb07b90e2d84f639056f49505
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 16:57:52
Display reorder
660,271,299,441,331,335,333,297,272,439,332,334,298,270,440,330,338,267,302,444,327,268,336,300,442,328,337,269,301,443,329,262,305,341,447,322,263,303,339,445,323,446,261,304,340,321,308,265,344,450,325,306,266,342,448,326,307,264,343,449,324,674,678,675,673,62,11,184,453,99,97,9,63,185,451,98,10,61,186,452,95,58,7,187,456,59,96,8,188,454,94,60,6,189,455,68,2,105,182,459,69,1,103,183,457,181,67,0,104,458,5,64,101,178,462,3,65,102,179,460,4,66,100,180,461,665,672,670,661,73,570,199,205,394,392,568,74,200,206,393,569,75,201,207,397,72,573,198,204,70,395,571,196,202,396,71,572,197,203,79,576,400,190,211,80,574,398,191,212,192,81,575,399,213,579,78,403,193,210,577,76,401,194,208,578,77,402,195,209,687,681,676,684,17,228,362,32,465,463,226,15,363,33,464,227,16,364,34,468,13,231,365,31,14,466,229,366,29,467,12,230,367,30,23,234,471,360,26,21,232,469,361,24,359,22,233,470,25,653,19,654,657,656,235,20,472,357,27,236,18,473,358,28,703,698,704,699,106,582,255,281,406,404,580,107,256,279,405,581,108,257,280,409,109,585,258,284,110,407,583,259,282,408,111,584,260,283,112,588,412,253,276,113,586,410,254,277,252,114,587,411,278,591,115,415,249,275,589,116,413,250,273,590,117,414,251,274,690,694,689,691,218,382,558,351,88,89,380,219,556,352,90,381,217,557,353,91,214,385,561,354,215,92,383,559,355,93,216,384,560,356,224,388,86,564,349,225,386,87,562,350,563,223,387,85,348,391,220,82,567,345,389,221,83,565,346,390,222,84,566,347,668,667,664,663,170,163,124,139,147,145,164,171,125,140,146,165,169,126,141,143,166,162,127,138,167,144,160,128,136,142,168,161,129,137,176,154,153,122,130,177,155,151,123,131,121,175,156,152,132,157,172,149,118,133,158,173,150,119,134,159,174,148,120,135,695,692,696,693,311,534,642,618,499,497,532,309,640,616,498,533,310,641,617,502,314,537,645,621,312,500,535,643,619,501,313,536,644,620,317,540,505,648,624,315,538,503,646,622,647,316,539,504,623,543,320,508,651,627,541,318,506,649,625,542,319,507,650,626,686,688,680,682,43,523,430,476,55,56,521,41,428,474,57,522,42,429,475,54,46,526,433,479,44,52,524,431,477,53,45,525,432,478,38,529,49,436,482,39,527,47,434,480,435,40,528,48,481,659,37,658,652,655,530,35,50,437,483,531,36,51,438,484,700,702,697,701,242,511,606,370,630,628,509,240,604,368,629,510,241,605,369,633,238,514,609,373,239,631,512,607,371,632,237,513,608,372,248,517,636,612,376,246,515,634,610,374,611,247,516,635,375,520,244,639,615,379,518,245,637,613,377,519,243,638,614,378,662,669,671,666,286,418,487,594,546,544,416,287,485,592,545,417,285,486,593,549,289,421,490,597,290,547,419,488,595,548,288,420,489,596,292,424,552,493,600,293,422,550,491,598,492,291,423,551,599,427,295,555,496,603,425,296,553,494,601,426,294,554,495,602,685,679,683,677 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#4af6d9f6d3730a7119657046629cd5cdd39170988afb99e43673591a2135edbf, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 16:57:53 · history