Equation 677 Database

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Magma 98fdef44d927…

magma 98fdef44d927
Size
705
Isomorphism class hash
98fdef44d927bd333311db7fbf00bc07680a8ffd7fcb2a7fb1692b93be1902e5
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 20:46:32
Display reorder
660,153,326,3,342,158,154,327,4,343,159,152,328,2,341,160,156,329,6,338,161,157,330,7,339,162,155,331,5,340,163,151,9,324,333,164,149,10,325,334,165,150,8,323,332,166,12,147,320,336,167,13,148,321,337,168,11,146,322,335,169,685,686,688,687,50,198,400,217,91,51,199,398,215,89,52,197,399,216,90,53,194,403,213,87,54,195,401,214,88,55,196,402,212,86,56,395,204,208,97,57,396,205,206,95,58,397,203,207,96,394,59,200,211,93,392,60,201,209,94,393,61,202,210,92,701,702,704,703,318,576,571,593,552,319,577,569,594,553,317,575,570,595,551,314,572,567,592,548,315,573,568,590,549,316,574,566,591,550,309,562,582,584,558,310,560,583,585,559,308,561,581,586,557,565,312,578,587,554,563,313,579,588,555,564,311,580,589,556,670,669,672,671,220,412,451,420,437,218,410,449,421,438,219,411,450,419,439,223,415,447,416,436,221,413,448,417,434,222,414,446,418,435,226,442,407,426,428,224,440,408,427,429,225,441,409,425,430,445,229,406,422,431,443,227,404,423,432,444,228,405,424,433,680,677,679,678,100,499,480,462,465,98,497,481,463,466,99,498,479,461,464,103,495,476,458,468,101,496,477,459,469,102,494,478,460,467,106,486,490,453,471,104,487,488,454,472,105,485,489,452,470,482,109,493,456,474,483,107,491,457,475,484,108,492,455,473,689,690,691,692,262,524,519,130,138,260,525,520,128,139,261,526,518,129,137,265,527,522,133,134,263,528,523,131,135,264,529,521,132,136,257,517,530,125,144,258,515,531,126,145,259,516,532,127,143,513,256,533,124,140,514,254,534,122,141,512,255,535,123,142,697,698,700,699,607,612,655,631,636,605,613,653,629,637,606,611,654,630,635,603,608,651,627,632,604,609,652,628,633,602,610,650,626,634,598,646,618,622,642,596,644,619,620,643,597,645,617,621,641,649,601,614,625,638,647,599,615,623,639,648,600,616,624,640,661,662,664,663,181,358,351,70,23,179,356,352,68,24,180,357,350,69,25,177,361,354,73,22,178,359,355,71,20,176,360,353,72,21,172,349,364,65,14,170,347,362,66,15,171,348,363,67,16,345,175,367,64,17,346,173,365,62,18,344,174,366,63,19,682,681,684,683,539,269,300,283,293,540,270,301,284,291,541,271,302,285,292,538,268,299,282,296,536,266,297,280,294,537,267,298,281,295,545,306,275,1,287,546,307,276,0,286,547,658,656,657,659,305,544,274,277,290,303,542,272,278,288,304,543,273,279,289,693,694,696,695,112,247,231,31,508,110,245,232,29,506,111,246,230,30,507,115,243,234,27,511,113,244,235,28,509,114,242,233,26,510,118,237,253,37,503,116,238,251,35,504,117,236,252,36,505,240,121,249,33,502,241,119,250,34,500,239,120,248,32,501,666,665,668,667,38,383,376,190,84,39,384,374,188,85,40,385,375,189,83,41,382,379,193,80,42,380,377,191,81,43,381,378,192,82,44,371,389,185,75,45,372,390,186,76,46,373,391,187,74,370,47,388,184,78,368,48,386,182,79,369,49,387,183,77,674,673,676,675 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#d3adc358e0fc62ec693454af0a9d8486ee65796d63279744faf9965dafec0a65, 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 20:46:33 · history