Equation 677 Database

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Magma d1ce8421f48a…

magma d1ce8421f48a
Size
705
Isomorphism class hash
d1ce8421f48ab78c368061e7096373edabf021008f875679dc24ac57c93d3fc9
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 18:18:17
Display reorder
660,373,315,363,275,16,316,17,374,364,276,314,15,372,365,274,369,12,318,366,271,370,13,319,367,272,371,14,317,368,273,22,321,361,379,281,23,322,362,380,282,21,320,360,378,280,18,324,357,375,277,376,19,325,358,278,20,323,359,377,279,685,686,688,687,157,468,187,167,185,469,186,158,188,168,470,184,159,189,166,160,181,467,190,163,161,182,465,191,164,162,183,466,192,165,176,474,193,155,173,177,475,194,156,174,175,476,195,154,172,179,473,196,151,169,152,180,471,197,170,178,472,198,153,171,701,702,704,703,309,355,270,576,247,356,248,310,268,574,354,249,308,269,575,312,250,351,266,579,313,251,352,267,577,311,252,353,265,578,253,346,261,307,571,254,347,259,305,572,255,345,260,306,573,256,349,264,303,570,304,257,350,262,568,258,348,263,302,569,670,669,672,671,24,478,60,207,129,479,130,25,61,205,477,131,26,62,206,27,128,481,63,210,28,126,482,64,208,29,127,480,65,209,120,484,66,30,202,121,485,67,31,203,122,483,68,32,204,123,487,69,33,201,34,124,488,70,199,125,486,71,35,200,680,677,679,678,496,2,72,221,224,1,225,497,73,222,0,223,495,74,220,499,227,5,75,217,500,228,3,76,218,498,226,4,77,219,230,8,78,494,212,231,6,79,492,213,229,7,80,493,211,233,11,81,490,215,491,234,9,82,216,232,10,83,489,214,689,690,691,692,529,40,522,546,554,41,552,530,523,547,39,553,528,524,548,525,550,36,521,545,526,551,37,519,543,527,549,38,520,544,560,46,513,535,537,558,47,514,536,538,559,45,515,534,539,556,42,516,531,540,532,557,43,517,541,555,44,518,533,542,697,698,700,699,601,580,639,607,616,581,617,602,637,608,582,618,603,638,609,600,619,583,635,606,598,620,584,636,604,599,621,585,634,605,622,586,630,592,613,623,587,628,593,614,624,588,629,594,615,625,589,633,595,612,596,626,590,631,610,627,591,632,597,611,661,662,664,663,387,326,292,397,414,327,415,388,293,398,328,416,389,294,396,390,413,329,291,393,391,411,330,289,394,392,412,331,290,395,405,332,283,385,403,406,333,284,386,404,407,334,285,384,402,408,335,286,381,399,382,409,336,287,400,410,337,288,383,401,682,681,684,683,341,54,564,298,134,55,135,342,562,296,56,133,343,563,297,340,137,57,567,301,338,138,58,565,299,339,136,59,566,300,646,52,647,645,644,132,53,561,344,295,641,51,642,640,643,658,48,659,656,657,648,650,49,651,649,654,50,655,652,653,693,694,696,695,242,507,117,85,100,508,101,243,118,86,509,99,241,119,84,245,96,510,116,88,246,97,511,114,89,244,98,512,115,87,106,505,108,240,91,107,506,109,238,92,105,504,110,239,90,102,501,111,236,94,237,103,502,112,95,104,503,113,235,93,666,665,668,667,438,150,417,446,462,148,463,439,418,444,149,464,440,419,445,437,461,146,420,442,435,459,147,421,443,436,460,145,422,441,453,141,423,429,452,454,139,424,430,450,455,140,425,431,451,456,144,426,432,448,433,457,142,427,449,458,143,428,434,447,674,673,676,675 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#789271f8e1620c5f8875a1b32dfd6da1b71c443ca3fc9082ace33bb0fcd8a22c, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 18:18:18 · history