Equation 677 Database

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Magma 334aef0f4e1d…

magma 334aef0f4e1d
Size
705
Isomorphism class hash
334aef0f4e1d8082e623a038a0c23f1149ae77ce5925dff6dfb1a90cfea6c039
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 17:38:39
Display reorder
660,323,335,358,347,13,321,333,14,359,345,322,334,12,357,346,319,331,16,354,343,320,332,17,355,344,318,330,15,356,342,364,329,341,19,353,327,339,20,365,351,328,340,18,363,352,337,325,22,360,349,338,326,23,361,350,336,324,21,362,348,685,686,688,687,211,218,137,125,431,212,216,429,135,123,210,217,430,136,124,214,221,427,133,121,215,219,428,134,122,213,220,426,132,120,143,209,224,437,131,207,222,435,141,129,208,223,436,142,130,227,205,433,139,127,225,206,434,140,128,226,204,432,138,126,701,702,704,703,559,564,39,64,317,560,565,315,40,65,558,566,316,41,63,562,567,313,38,60,563,568,314,36,61,561,569,312,37,62,45,557,570,308,70,555,571,306,46,71,556,572,307,47,69,573,553,311,44,66,574,554,309,42,67,575,552,310,43,68,670,669,672,671,155,166,235,101,439,153,167,440,236,99,154,165,438,234,100,151,162,442,238,97,152,163,443,239,98,150,164,441,237,96,233,146,157,445,107,144,158,446,231,105,145,156,444,232,106,160,149,448,229,103,161,147,449,230,104,159,148,447,228,102,680,677,679,678,463,79,457,246,109,464,80,110,458,247,462,78,108,456,248,466,82,112,460,249,467,83,113,461,250,465,81,111,459,251,455,469,77,115,244,470,75,116,453,245,468,76,114,454,243,73,472,118,451,240,74,473,119,452,241,72,471,117,450,242,689,690,691,692,503,513,490,533,291,501,514,292,491,531,502,515,293,489,532,499,512,290,486,529,500,510,288,487,530,498,511,289,488,528,496,509,519,297,524,507,520,298,497,522,508,521,299,495,523,518,505,296,492,527,516,506,294,493,525,517,504,295,494,526,697,698,700,699,599,609,635,623,585,597,610,586,633,621,598,611,587,634,622,595,608,584,631,619,596,606,582,632,620,594,607,583,630,618,626,590,600,576,614,588,601,577,624,612,589,602,578,625,613,603,593,579,629,617,604,591,580,627,615,605,592,581,628,616,661,662,664,663,34,175,374,182,8,35,176,6,372,180,33,174,7,373,181,30,178,11,377,185,31,179,9,375,183,32,177,10,376,184,369,25,173,3,188,26,171,4,370,186,24,172,5,371,187,169,28,2,368,191,170,29,1,366,189,168,27,0,367,190,682,681,684,683,544,546,300,537,84,545,547,85,301,538,543,548,86,302,539,540,549,87,303,536,541,550,88,304,534,542,551,89,305,535,641,642,643,90,640,646,647,91,645,644,637,638,92,636,639,655,654,93,652,653,659,658,94,657,656,651,650,95,648,649,693,694,696,695,254,267,482,286,59,252,268,57,480,287,253,269,58,481,285,257,266,55,485,282,255,264,56,483,283,256,265,54,484,284,477,260,273,50,277,258,274,48,478,278,259,275,49,479,276,272,263,53,476,280,270,261,51,474,281,271,262,52,475,279,666,665,668,667,413,423,399,389,198,411,424,199,400,387,412,425,200,401,388,409,422,201,398,385,410,420,202,396,386,408,421,203,397,384,390,404,414,196,380,402,415,197,391,378,403,416,195,392,379,417,407,192,393,383,418,405,193,394,381,419,406,194,395,382,674,673,676,675 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#5c1fa523b4d9d2fbb415708ccaff34546079d57eeb66e712dcba93d7172179c8, 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 17:38:40 · history