Equation 677 Database

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Magma fab14fe167d6…

magma fab14fe167d6
Size
705
Isomorphism class hash
fab14fe167d6bd3a7577a5928550ae785ddff920b6a5166a580bf01e6d4f0f87
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 20:00:52
Display reorder
660,235,234,236,237,238,239,232,233,231,228,229,230,397,398,396,400,401,399,403,404,402,406,407,405,266,264,265,269,267,268,272,270,271,275,273,274,241,242,240,244,245,243,247,248,246,250,251,249,254,252,253,257,255,256,260,258,259,263,261,262,671,688,680,696,369,371,370,367,368,366,362,360,361,365,363,364,42,43,44,45,46,47,40,41,39,36,37,38,349,350,348,352,353,351,355,356,354,358,359,357,374,372,373,377,375,376,380,378,379,383,381,382,346,347,345,342,343,344,337,338,336,340,341,339,686,700,691,701,137,136,135,132,133,134,142,143,141,138,139,140,77,75,76,73,74,72,83,81,82,79,80,78,391,392,390,394,395,393,389,387,388,385,386,384,145,146,144,148,149,147,151,152,150,154,155,153,4,5,3,1,0,2,10,11,9,6,7,8,664,675,668,679,429,431,430,427,428,426,422,420,421,425,423,424,70,71,69,66,67,68,61,62,60,64,65,63,456,457,458,459,460,461,462,463,464,465,466,467,434,432,433,437,435,436,440,438,439,443,441,442,446,444,445,449,447,448,452,450,451,455,453,454,673,689,681,690,515,514,513,510,511,512,505,506,504,508,509,507,524,522,523,527,525,526,519,520,521,518,516,517,501,502,503,500,498,499,492,493,494,495,496,497,470,468,469,473,471,472,476,474,475,479,477,478,480,481,482,483,484,485,486,487,488,489,490,491,685,699,695,704,618,620,619,623,621,622,615,616,617,614,612,613,16,17,15,12,13,14,22,23,21,18,19,20,605,603,604,601,602,600,611,609,610,607,608,606,579,580,581,578,576,577,585,586,587,584,582,583,591,592,593,590,588,589,597,598,599,596,594,595,684,698,692,702,204,206,205,209,207,208,212,210,211,215,213,214,168,169,170,171,172,173,174,175,176,177,178,179,192,193,194,195,196,197,198,199,200,201,202,203,227,225,226,223,224,222,218,216,217,221,219,220,184,185,183,180,181,182,190,191,189,186,187,188,661,666,662,667,298,297,299,296,294,295,288,289,290,291,292,293,409,410,408,412,413,411,415,416,414,418,419,417,277,278,276,280,281,279,283,284,282,286,287,285,310,311,309,306,307,308,301,302,300,304,305,303,322,323,321,318,319,320,313,314,312,316,317,315,672,687,682,694,131,130,129,126,127,128,121,122,120,124,125,123,54,55,56,57,58,59,52,53,51,48,49,50,658,659,657,654,655,656,649,650,648,652,653,651,631,632,630,634,635,633,629,627,628,625,626,624,644,642,643,647,645,646,639,640,641,638,636,637,683,697,693,703,547,546,548,549,550,551,544,545,543,540,541,542,25,26,24,28,29,27,31,32,30,34,35,33,533,531,532,529,530,528,539,537,538,535,536,534,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,665,676,670,678,94,93,95,92,90,91,84,85,86,87,88,89,162,163,164,165,166,167,160,161,159,156,157,158,332,330,331,335,333,334,327,328,329,326,324,325,106,107,105,102,103,104,97,98,96,100,101,99,117,118,119,116,114,115,108,109,110,111,112,113,663,674,669,677 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {63} 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 20:00:53 · history