Equation 677 Database

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Magma 9caab7130085…

magma 9caab7130085
Size
705
Isomorphism class hash
9caab71300855e12cec9247d588bb7622d24c34cf8a02fa6b5dcdee0d4af3d05
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 19:46:05
Display reorder
660,287,191,622,187,616,620,288,185,614,192,621,193,289,186,615,190,625,286,183,619,188,623,284,184,617,189,624,285,182,618,178,197,293,628,611,198,294,626,176,612,199,295,627,177,613,292,196,631,181,610,290,194,629,179,608,291,195,630,180,609,687,688,686,685,426,326,349,367,342,347,427,365,343,327,348,328,425,366,341,329,345,422,363,338,330,346,423,364,339,331,344,424,362,340,358,324,417,355,333,325,418,353,356,334,323,416,354,357,332,420,320,351,361,336,421,321,352,359,337,419,322,350,360,335,703,704,701,702,175,272,596,268,592,597,173,266,590,273,598,274,174,267,591,275,599,171,271,595,276,600,172,269,593,277,601,170,270,594,263,278,166,602,587,279,164,603,264,588,280,165,604,265,589,169,281,605,262,586,167,282,606,260,584,168,283,607,261,585,671,672,670,669,61,134,88,96,434,89,62,97,435,135,87,136,60,98,436,137,84,64,99,437,138,85,65,100,438,139,86,63,101,439,102,132,67,94,432,133,68,95,103,433,131,66,93,104,431,70,128,90,105,428,71,129,91,106,429,69,130,92,107,430,679,680,678,677,142,455,485,441,464,486,140,442,465,456,487,457,141,440,466,454,484,145,444,467,452,482,143,445,468,453,483,144,443,469,447,461,148,476,470,462,146,477,448,471,463,147,478,446,472,151,460,479,450,473,149,458,480,451,474,150,459,481,449,475,692,691,690,689,108,239,217,234,542,215,109,235,543,240,216,241,110,233,544,238,213,111,230,545,236,214,112,231,546,237,212,113,232,547,225,245,114,223,540,246,115,221,226,541,247,116,222,224,539,117,244,219,228,536,118,242,220,229,537,119,243,218,227,538,699,700,698,697,57,80,36,22,27,37,58,23,28,78,38,79,59,21,29,83,39,56,18,26,81,40,54,19,24,82,41,55,20,25,13,75,48,42,33,76,49,43,14,34,77,50,44,12,35,51,74,45,16,32,52,72,46,17,30,53,73,47,15,31,663,664,662,661,210,646,7,640,302,8,211,638,303,644,11,645,209,639,304,649,9,206,643,305,647,10,207,641,306,648,1,208,642,307,635,652,201,0,300,650,202,2,636,301,651,200,3,637,299,204,655,4,634,296,205,653,5,632,297,203,654,6,633,298,682,683,684,681,255,561,574,555,565,575,256,556,566,559,573,560,254,554,564,121,577,258,558,562,657,658,259,656,659,120,576,257,557,563,553,124,253,579,571,122,251,580,551,572,123,252,578,552,570,249,127,582,549,567,250,125,583,550,568,248,126,581,548,569,695,696,693,694,152,528,504,513,489,505,153,514,490,529,503,527,154,512,488,524,500,155,516,492,525,501,156,517,493,526,502,157,515,491,519,534,158,510,495,535,159,511,520,496,533,160,509,518,494,161,530,506,522,498,162,531,507,523,499,163,532,508,521,497,667,668,665,666,314,405,390,395,374,391,315,396,375,406,389,404,316,397,376,408,386,317,394,377,409,387,318,392,378,407,388,319,393,379,401,411,312,381,372,412,313,382,402,373,410,311,380,403,371,308,414,384,400,368,309,415,385,398,369,310,413,383,399,370,675,676,673,674 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#a96a88e4cf05ff772a659e73be5ebad0179d3b86aa5fbe0be371d7ceb3ac096d, 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 19:46:05 · history