Equation 677 Database

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Magma a4c89d88eb04…

magma a4c89d88eb04
Size
705
Isomorphism class hash
a4c89d88eb04834ef34c7761927bbe71f4baacfaa60343f0579ebca785ff09c1
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 19:54:08
Display reorder
660,300,262,320,286,274,298,263,275,321,287,299,264,276,319,288,265,303,277,316,289,266,301,278,317,290,267,302,279,318,291,268,306,280,311,292,269,304,281,312,293,270,305,282,310,294,309,271,283,314,295,315,307,272,284,296,308,273,285,313,297,685,686,688,687,140,383,98,123,107,141,384,108,99,121,139,382,106,97,122,386,136,110,94,119,387,137,111,95,120,385,138,109,96,118,389,131,113,104,129,390,132,114,105,127,388,130,112,103,128,134,392,116,100,125,101,135,393,117,126,133,391,115,102,124,701,702,704,703,589,257,552,582,562,587,258,560,553,583,588,256,561,551,581,260,585,565,548,578,261,586,563,549,579,259,584,564,550,580,255,595,568,558,573,253,593,566,559,574,254,594,567,557,572,591,251,571,554,576,555,592,252,569,577,590,250,570,556,575,670,669,672,671,405,150,417,440,429,403,148,427,415,441,404,149,428,416,439,153,401,425,413,436,151,402,426,414,437,152,400,424,412,438,145,396,420,408,431,146,394,418,406,432,147,395,419,407,430,399,144,423,411,434,409,397,142,421,435,398,143,422,410,433,680,677,679,678,450,165,458,478,466,448,163,467,459,479,449,164,468,457,480,161,453,469,454,481,162,451,470,455,482,160,452,471,456,483,156,445,472,464,484,154,446,473,465,485,155,447,474,463,486,444,159,475,460,487,461,442,157,476,488,443,158,477,462,489,689,690,691,692,230,504,69,222,21,231,502,22,70,220,229,503,23,71,221,507,226,20,68,225,505,227,18,66,223,506,228,19,67,224,510,236,12,60,217,508,237,13,61,218,509,235,14,62,219,232,513,15,63,216,64,233,511,16,214,234,512,17,65,215,697,698,700,699,643,605,655,631,610,641,606,608,653,629,642,607,609,654,630,604,639,613,651,627,602,640,611,652,628,603,638,612,650,626,596,634,616,646,622,597,632,614,644,620,598,633,615,645,621,637,599,619,649,625,647,635,600,617,623,636,601,618,648,624,661,662,664,663,330,32,338,360,346,328,30,347,339,358,329,31,348,337,359,35,333,349,334,363,33,331,350,335,361,34,332,351,336,362,27,325,352,344,366,28,326,353,345,364,29,327,354,343,365,324,26,355,340,369,341,322,24,356,367,323,25,357,342,368,682,681,684,683,545,245,517,536,79,546,246,80,518,534,547,244,81,519,535,248,544,78,516,532,249,542,76,514,533,247,543,77,515,531,243,537,525,523,527,241,538,72,524,526,242,658,657,656,659,539,239,73,522,530,520,540,240,74,528,541,238,75,521,529,693,694,696,695,183,490,199,174,204,181,491,202,200,172,182,492,203,201,173,493,179,207,198,177,494,180,205,196,175,495,178,206,197,176,496,189,210,190,169,497,187,208,191,170,498,188,209,192,171,185,499,213,193,168,194,186,500,211,166,184,501,212,195,167,666,665,668,667,59,82,11,47,378,57,83,376,9,45,58,84,377,10,46,85,55,381,7,43,86,56,379,8,44,87,54,380,6,42,88,50,373,2,38,89,48,374,1,36,90,49,375,0,37,53,91,372,5,41,3,51,92,370,39,52,93,371,4,40,674,673,676,675 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#b356224f433e80b1c4ac338e7aaea2066ee34f4a7233e2d09dbcc6e7070accf0, 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 19:54:09 · history