Equation 677 Database

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Magma 4ecbd74dbb30…

magma 4ecbd74dbb30
Size
705
Isomorphism class hash
4ecbd74dbb30f0997c00da985d31666de2d27f9c82ba3299c0576eb4df8f4e7d
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 21:51:48
Display reorder
660,27,113,285,98,277,28,278,111,286,96,112,276,29,287,97,26,109,280,284,101,24,110,281,282,99,25,108,279,283,100,104,275,291,18,93,273,102,292,19,94,20,274,103,293,95,107,271,290,21,92,105,272,288,22,90,106,270,289,23,91,685,686,688,687,436,84,425,398,413,437,411,85,423,396,86,412,435,424,397,432,87,409,421,401,433,88,410,422,399,434,89,408,420,400,82,404,416,427,393,402,83,414,428,394,426,403,81,415,395,78,407,419,430,392,79,405,417,431,390,80,406,418,429,391,701,702,704,703,258,584,248,231,236,259,234,585,246,232,583,235,260,247,233,261,580,239,251,230,262,581,237,249,228,263,582,238,250,229,590,242,254,264,222,240,591,252,265,223,266,241,589,253,224,586,245,257,267,225,587,243,255,268,226,588,244,256,269,227,670,669,672,671,53,172,41,64,444,51,445,170,39,65,171,446,52,40,63,49,175,447,37,60,50,173,448,38,61,48,174,449,36,62,167,442,32,44,55,443,168,30,42,56,43,441,169,31,54,166,438,35,47,58,164,439,33,45,59,165,440,34,46,57,680,677,679,678,464,72,452,476,487,462,488,73,450,474,74,486,463,451,475,467,75,490,455,479,465,76,491,453,477,466,77,489,454,478,70,493,458,470,482,494,71,456,468,480,469,492,69,457,481,66,496,461,473,485,67,497,459,471,483,68,495,460,472,484,689,690,691,692,210,145,192,553,561,211,562,146,193,554,144,563,209,191,552,206,148,560,188,556,207,149,558,189,557,208,147,559,190,555,143,567,198,201,551,568,141,199,202,549,200,569,142,197,550,139,566,194,204,547,140,564,195,205,548,138,565,196,203,546,697,698,700,699,614,596,651,620,639,615,637,597,649,621,595,638,613,650,619,610,592,635,647,616,611,593,636,648,617,612,594,634,646,618,602,630,642,605,626,628,603,640,606,627,604,629,601,641,625,598,633,645,608,622,599,631,643,609,623,600,632,644,607,624,661,662,664,663,333,118,318,303,308,334,306,119,319,304,117,307,335,320,305,332,114,311,321,302,330,115,309,322,300,331,116,310,323,301,124,314,324,339,294,312,125,325,340,295,341,313,123,326,296,120,317,327,338,297,121,315,328,336,298,122,316,329,337,299,682,681,684,683,3,7,155,575,212,4,213,8,153,576,6,214,5,154,574,2,10,215,151,578,1,11,216,152,579,0,9,217,150,577,13,658,656,657,659,218,14,159,160,570,653,654,12,652,655,16,219,157,162,573,17,220,158,163,571,15,221,156,161,572,693,694,696,695,506,182,536,519,523,504,524,183,534,520,184,522,505,535,521,509,185,526,539,518,507,186,527,537,516,508,187,525,538,517,180,529,542,501,510,530,181,540,502,511,503,528,179,541,512,176,532,545,500,513,177,533,543,498,514,178,531,544,499,515,666,665,668,667,389,129,377,346,365,387,363,130,375,347,131,364,388,376,345,385,128,361,373,342,386,126,362,374,343,384,127,360,372,344,135,356,368,380,352,354,136,366,378,353,379,355,137,367,351,134,359,371,383,348,132,357,369,381,349,133,358,370,382,350,674,673,676,675 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#f80d3e42bb36c9de3f16a7272ddaae8a1c868ead8083a2f830ed5472d041fc61, 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 21:51:49 · history