Equation 677 Database

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Magma 0b9f6ce09a38…

magma 0b9f6ce09a38
Size
705
Isomorphism class hash
0b9f6ce09a38863ce82a498938943d23a13e5188af24cd2504431ed31798d94e
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 18:21:52
Display reorder
660,276,599,617,621,590,277,600,618,622,591,620,601,278,619,592,598,279,616,624,593,596,280,614,625,594,597,281,615,623,595,282,605,608,627,588,283,606,609,628,589,284,607,610,626,587,604,285,611,630,584,602,286,612,631,585,603,287,613,629,586,687,688,686,685,171,406,154,378,387,169,407,155,379,388,380,405,170,156,389,402,167,157,381,386,403,168,158,382,384,404,166,159,383,385,177,397,160,376,393,175,398,161,377,394,176,396,162,375,395,400,173,163,372,392,401,174,164,373,390,399,172,165,374,391,703,704,701,702,271,569,572,542,551,272,570,573,543,552,544,571,270,574,553,568,274,575,545,550,566,275,576,546,548,567,273,577,547,549,269,560,578,540,557,267,561,579,541,558,268,562,580,539,559,563,265,581,536,556,564,266,582,537,554,565,264,583,538,555,671,672,670,669,145,187,191,212,414,146,188,192,213,415,211,189,147,190,416,186,144,194,208,417,184,142,195,209,418,185,143,193,210,419,151,178,197,203,412,152,179,198,204,413,153,180,196,202,411,181,150,200,206,408,182,148,201,207,409,183,149,199,205,410,679,680,678,677,223,445,465,421,441,224,446,466,422,442,420,444,225,467,443,448,222,464,424,440,449,220,462,425,438,447,221,463,423,439,214,451,456,427,432,215,452,457,428,433,216,450,458,426,434,454,217,459,430,435,455,218,460,431,436,453,219,461,429,437,692,691,690,689,524,69,2,128,244,522,70,3,129,245,130,68,523,4,246,72,527,5,131,247,73,525,6,132,248,71,526,7,133,249,519,67,8,126,242,520,65,9,127,243,521,66,10,125,241,63,518,11,122,238,64,516,12,123,239,62,517,13,124,240,699,700,698,697,18,33,81,86,102,19,34,82,87,103,88,32,17,80,101,36,14,84,89,98,37,15,85,90,99,35,16,83,91,100,24,31,79,92,108,25,29,77,93,109,23,30,78,94,107,27,20,75,95,104,28,21,76,96,105,26,22,74,97,106,663,664,662,661,634,309,313,335,291,632,310,314,333,292,334,311,633,312,293,308,637,316,331,290,306,635,317,332,288,307,636,315,330,289,640,300,319,326,297,638,301,320,324,298,639,302,318,325,299,303,643,322,329,296,304,641,323,327,294,305,642,321,328,295,682,683,684,681,40,657,659,658,656,38,648,651,650,649,654,653,39,655,652,0,43,535,257,141,645,41,646,644,647,1,42,534,256,140,46,259,533,255,139,44,260,531,253,137,45,258,532,254,138,262,49,529,251,135,263,47,530,252,136,261,48,528,250,134,695,696,693,694,230,473,485,497,507,231,471,483,495,508,496,472,229,484,509,469,226,481,493,506,470,227,482,494,504,468,228,480,492,505,236,479,491,503,513,237,477,489,501,514,235,478,490,502,515,475,232,487,499,512,476,233,488,500,510,474,234,486,498,511,667,668,665,666,111,53,343,350,362,112,54,344,348,360,349,55,110,342,361,52,114,346,353,365,50,115,347,351,363,51,113,345,352,364,117,59,341,356,368,118,60,339,354,366,116,61,340,355,367,58,120,337,359,371,56,121,338,357,369,57,119,336,358,370,675,676,673,674 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#7d1a9ea30af90bcd4d08abf0386c83ad32096e29a3d77362c99ba04d722859db, 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 18:21:53 · history