Equation 677 Database

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Magma 182513949b39…

magma 182513949b39
Size
705
Isomorphism class hash
182513949b39d031fee5efc455412f32d2f34d9d3bcddcb9a3adec1f89deae90
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 19:16:04
Display reorder
660,205,306,312,285,277,307,206,278,313,286,276,204,308,314,287,201,305,273,311,288,202,303,274,309,289,203,304,275,310,290,211,297,283,318,291,212,298,284,319,292,210,299,282,320,293,300,207,279,317,294,315,301,208,280,295,302,209,281,316,296,685,686,688,687,136,455,418,445,438,453,137,439,419,446,440,135,454,417,444,139,458,437,421,441,140,456,435,422,442,138,457,436,420,443,134,461,429,424,451,132,459,430,425,452,133,460,431,423,450,464,130,432,427,447,428,462,131,433,448,463,129,434,426,449,701,702,704,703,271,585,607,576,569,586,272,570,605,577,571,270,584,606,575,267,588,568,603,572,268,589,566,604,573,269,587,567,602,574,262,591,560,598,582,263,592,561,596,583,261,590,562,597,581,594,265,563,601,578,599,595,266,564,579,593,264,565,600,580,670,669,672,671,52,9,472,155,151,10,53,152,473,153,150,51,11,471,154,55,8,147,475,158,56,6,148,476,156,54,7,149,474,157,50,1,142,470,161,48,0,143,468,159,49,2,141,469,160,3,46,145,466,164,467,4,47,146,162,5,45,144,465,163,680,677,679,678,172,116,121,483,57,114,173,58,122,484,59,171,115,120,485,175,112,60,117,486,176,113,61,118,487,174,111,62,119,488,170,107,63,127,481,168,105,64,128,482,169,106,65,126,480,110,166,66,123,477,124,108,167,67,478,109,165,68,125,479,689,690,691,692,198,241,77,545,92,242,199,90,75,543,91,200,240,76,544,197,237,88,80,548,195,238,89,78,546,196,239,87,79,547,189,247,83,72,540,190,248,81,73,541,191,246,82,74,542,243,192,86,71,539,69,244,193,84,537,245,194,85,70,538,697,698,700,699,95,633,655,630,616,634,93,614,653,631,615,94,632,654,629,98,636,619,651,626,96,637,617,652,627,97,635,618,650,628,101,639,611,646,621,99,640,612,644,622,100,638,613,645,620,642,104,610,649,624,647,643,102,608,625,641,103,609,648,623,661,662,664,663,220,337,346,332,368,338,221,366,347,330,367,219,336,345,331,223,333,364,349,328,224,334,365,350,329,222,335,363,348,327,218,343,359,352,323,216,344,357,353,321,217,342,358,351,322,339,214,362,355,326,356,340,215,360,324,341,213,361,354,325,682,681,684,683,257,30,554,24,40,31,255,41,555,25,39,256,32,556,26,260,29,43,557,23,258,27,44,558,21,259,28,42,559,22,252,36,38,552,17,253,37,12,553,16,254,656,657,658,659,35,251,13,549,18,550,33,249,14,19,34,250,15,551,20,693,694,696,695,184,501,523,499,527,502,185,525,524,500,526,183,503,522,498,187,504,530,519,495,188,505,528,520,496,186,506,529,521,497,182,507,533,514,490,180,508,531,515,491,181,509,532,513,489,510,178,536,517,493,518,511,179,534,494,512,177,535,516,492,666,665,668,667,228,395,405,383,371,393,229,369,406,381,370,230,394,407,382,227,398,374,408,386,225,396,372,409,384,226,397,373,410,385,234,401,377,411,389,235,399,375,412,387,236,400,376,413,388,404,233,380,414,392,415,402,231,378,390,403,232,379,416,391,674,673,676,675 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#96b025dbf47c4a59dfaaf1b34262061bd74b6a84a8a9978c39bcd4e78b704a7c, 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 19:16:05 · history