Equation 677 Database

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Magma 76029794faa5…

magma 76029794faa5
Size
705
Isomorphism class hash
76029794faa51c56e2525ebb3e528ffa52af51c2f6f60c9e702aa0cb1f982436
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 15:08:00
Display reorder
660,635,103,620,630,631,655,104,640,650,651,615,600,610,611,102,106,555,541,550,551,107,575,561,570,571,105,595,581,590,591,455,101,444,451,452,475,99,461,470,471,435,100,421,430,431,510,97,515,500,511,98,535,520,530,531,96,495,480,490,491,691,689,702,697,632,126,636,621,629,652,127,656,641,649,612,616,601,609,128,129,552,556,540,549,130,572,576,560,569,131,592,596,580,589,453,124,456,443,450,472,125,476,460,469,432,123,436,420,429,501,120,512,516,509,121,532,536,521,529,122,492,496,481,489,701,686,698,694,274,191,382,250,346,275,189,383,251,347,273,381,249,345,190,187,270,378,246,342,188,271,379,247,343,186,272,380,248,344,265,182,373,241,337,266,180,374,242,338,264,181,372,240,336,244,185,268,376,340,183,269,377,245,341,184,267,375,243,339,673,663,677,666,370,70,394,310,334,371,71,395,311,335,369,393,309,333,69,66,366,390,306,330,67,367,391,307,331,68,368,392,308,332,361,61,385,301,325,362,62,386,302,326,360,60,384,300,324,304,64,364,388,328,65,365,389,305,329,63,363,387,303,327,671,669,678,676,639,144,628,627,633,659,145,648,647,653,619,608,607,613,146,147,559,548,547,553,148,579,568,567,573,149,599,588,587,593,459,150,449,448,454,479,151,468,467,473,439,152,428,427,433,507,153,519,508,513,154,539,528,527,533,155,499,488,487,493,695,692,687,688,626,34,638,625,634,646,35,658,645,654,606,618,605,614,33,30,546,558,545,554,31,566,578,565,574,32,586,598,585,594,458,25,442,440,441,466,26,478,465,474,426,24,438,425,434,505,28,506,518,514,29,526,538,525,534,27,486,498,485,494,696,690,700,703,637,41,623,622,624,657,39,643,642,644,617,603,602,604,40,37,557,543,542,544,38,577,563,562,564,36,597,583,582,584,457,47,446,445,447,477,45,463,462,464,437,46,423,422,424,502,43,517,503,504,44,537,523,522,524,42,497,483,482,484,693,704,685,699,141,48,262,176,203,142,49,263,174,201,143,261,175,202,50,51,140,258,179,199,52,138,259,177,200,53,139,260,178,198,132,54,253,171,194,133,55,254,172,192,134,56,252,173,193,170,57,135,256,197,58,136,257,168,195,59,137,255,169,196,679,672,665,662,78,23,298,322,87,79,21,299,323,88,80,297,321,89,22,19,81,294,318,86,20,82,295,319,84,18,83,296,320,85,76,14,289,313,93,77,12,290,314,94,75,13,288,312,95,316,17,72,292,92,15,73,293,317,90,16,74,291,315,91,675,670,668,681,234,112,358,10,406,235,113,359,11,407,236,357,9,405,111,108,237,354,6,402,109,238,355,7,403,110,239,356,8,404,232,118,349,0,397,233,119,350,2,398,231,117,348,1,396,4,114,228,352,400,115,229,353,5,401,116,230,351,3,399,682,680,674,684,286,156,206,226,418,287,157,204,227,419,285,205,225,417,158,159,282,209,222,414,160,283,207,223,415,161,284,208,224,416,277,162,212,217,409,278,163,210,218,410,276,164,211,216,408,220,165,280,215,412,166,281,213,221,413,167,279,214,219,411,683,661,664,667 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#055eb219830141adc126b0e3c095dec26895b5c9338d223a671ccb522fe00e95, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 15:08:02 · history