Equation 677 Database

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Magma 3e2d1d0a306e…

magma 3e2d1d0a306e
Size
705
Isomorphism class hash
3e2d1d0a306ed219c82dfa22dce3c004248c889353583b598a066c0e379ef2a0
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 17:19:23
Display reorder
660,416,420,610,202,184,414,421,608,203,185,415,422,609,201,183,419,423,613,198,180,611,424,417,199,181,425,418,612,200,182,411,426,616,193,190,412,427,614,194,191,413,428,615,192,189,429,410,619,196,186,430,408,617,197,187,431,409,618,195,188,687,688,686,685,506,235,290,500,73,504,236,288,498,74,505,234,289,499,72,509,238,293,503,76,291,239,507,501,77,237,508,292,502,75,512,233,296,495,79,510,231,294,496,80,511,232,295,497,78,229,515,299,494,82,230,513,297,492,83,228,514,298,493,81,703,704,701,702,380,385,179,603,396,378,386,177,604,397,379,384,178,602,398,383,388,175,606,399,176,389,381,607,400,387,382,174,605,401,375,391,170,601,402,376,392,168,599,403,377,390,169,600,404,394,374,173,597,405,395,372,171,598,406,393,373,172,596,407,671,672,670,669,307,323,524,134,241,308,321,522,132,242,306,322,523,133,240,310,319,527,130,244,525,320,311,131,245,318,309,526,129,243,305,314,519,125,247,303,312,520,123,248,304,313,521,124,246,317,301,518,128,250,315,302,516,126,251,316,300,517,127,249,679,680,678,677,259,274,333,535,287,260,275,334,536,285,258,273,335,534,286,262,270,332,538,283,330,271,263,539,284,272,261,331,537,282,257,265,324,533,278,255,266,325,531,276,256,264,326,532,277,268,253,327,529,281,269,254,328,530,279,267,252,329,528,280,692,691,690,689,2,356,579,101,153,1,354,580,99,154,0,355,581,100,155,5,359,578,97,156,576,357,3,98,157,358,4,577,96,158,8,351,585,107,151,6,352,586,105,152,7,353,587,106,150,350,11,584,103,147,348,9,582,104,148,349,10,583,102,149,699,700,698,697,53,65,13,36,25,51,63,14,37,26,52,64,12,38,24,49,61,16,39,28,17,62,50,40,29,60,48,15,41,27,59,71,19,42,31,57,69,20,43,32,58,70,18,44,30,67,55,22,45,34,68,56,23,46,35,66,54,21,47,33,663,664,662,661,634,212,433,628,87,632,210,434,626,88,633,211,432,627,89,637,215,436,631,86,437,213,635,629,84,214,636,435,630,85,640,207,439,623,93,638,208,440,624,94,639,209,438,625,95,206,643,442,622,92,204,641,443,620,90,205,642,441,621,91,682,683,684,681,659,657,368,658,656,651,648,366,650,649,655,653,367,654,652,595,108,371,166,115,369,645,646,644,647,167,594,370,165,116,593,109,363,164,118,591,110,364,162,119,592,111,365,163,117,112,589,362,160,121,113,590,360,161,122,114,588,361,159,120,695,696,693,694,574,341,137,562,547,575,339,135,563,548,573,340,136,561,546,570,337,140,558,550,138,338,571,559,551,336,572,139,560,549,565,347,143,553,545,566,345,141,554,543,564,346,142,552,544,343,568,146,556,541,344,569,144,557,542,342,567,145,555,540,667,668,665,666,466,477,227,448,482,467,478,225,449,480,465,479,226,447,481,462,476,223,444,485,224,474,463,445,483,475,464,222,446,484,457,468,218,454,488,458,469,216,455,486,456,470,217,453,487,471,460,221,450,491,472,461,219,451,489,473,459,220,452,490,675,676,673,674 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#4ddcb3732d8cead11c348e4cf9e2318d25466469e5bf7b5d48d8ea06dbb2e5f3, 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 17:19:24 · history