Equation 677 Database

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Magma 8af84b556b80…

magma 8af84b556b80
Size
705
Isomorphism class hash
8af84b556b80c1a1c4c5a5532c3263cf1b0fb9368b4a8dd504f69633f332c9d7
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 20:32:05
Display reorder
704,26,84,53,65,24,85,51,63,25,86,52,64,29,87,49,61,27,88,50,62,28,89,48,60,32,90,59,71,30,91,57,69,31,92,58,70,93,35,55,67,94,33,56,68,34,95,54,66,77,75,76,73,74,72,83,81,78,79,80,82,703,700,702,701,659,657,658,656,651,648,650,649,655,653,654,652,643,641,642,640,647,645,646,644,639,637,638,636,623,620,622,621,615,612,614,613,619,616,618,617,632,635,634,633,625,627,626,624,631,628,630,629,450,451,452,453,454,455,448,449,446,444,445,447,691,688,690,689,243,308,320,332,244,306,318,330,245,307,319,331,242,311,323,335,240,309,321,333,241,310,322,334,249,303,315,327,250,304,316,328,251,305,317,329,302,248,314,326,300,246,312,324,247,301,313,325,344,342,343,347,345,346,339,340,337,338,336,341,672,675,673,674,225,137,147,113,226,135,148,111,227,136,149,112,224,133,146,109,222,134,144,110,223,132,145,108,216,143,153,119,217,141,154,117,218,142,155,118,139,219,152,115,140,220,150,116,221,138,151,114,123,124,125,122,120,121,129,130,127,128,126,131,681,682,680,683,103,414,429,432,104,415,430,433,102,416,431,434,106,417,428,435,107,418,426,436,105,419,427,437,101,412,420,438,99,413,421,439,100,411,422,440,408,97,423,441,409,98,424,442,96,410,425,443,400,401,399,396,397,398,406,407,404,402,403,405,693,695,694,692,166,191,193,209,167,189,194,207,165,190,192,208,162,187,196,205,163,188,197,206,164,186,195,204,157,182,199,215,158,180,200,213,156,181,198,214,185,160,202,211,183,161,203,212,159,184,201,210,175,176,174,178,179,177,173,171,168,169,170,172,698,696,699,697,36,593,554,574,37,591,552,575,38,592,553,573,39,589,557,570,40,590,555,571,41,588,556,572,42,599,560,565,43,597,558,566,44,598,559,564,595,45,563,568,596,46,561,569,47,594,562,567,584,582,583,587,585,586,579,580,577,578,576,581,684,686,687,685,18,376,386,353,19,377,384,351,20,375,385,352,21,372,389,349,22,373,387,350,23,374,388,348,16,382,392,359,17,383,390,357,15,381,391,358,378,12,395,355,379,13,393,356,14,380,394,354,363,364,365,362,360,361,369,370,367,368,366,371,661,662,660,663,239,254,273,278,237,252,274,276,238,253,275,277,235,257,272,281,236,255,270,279,234,256,271,280,230,260,264,284,228,258,265,282,229,259,266,283,263,233,267,287,261,231,268,285,232,262,269,286,298,299,297,294,295,296,289,290,291,292,293,288,676,679,677,678,5,486,503,458,3,487,501,456,4,488,502,457,0,489,499,461,2,490,500,459,1,491,498,460,11,484,494,464,9,485,492,462,10,483,493,463,480,7,497,467,481,8,495,465,6,482,496,466,479,477,478,475,476,474,470,468,472,473,471,469,665,666,664,667,603,508,516,539,604,509,517,537,605,507,518,538,602,504,519,535,600,505,520,536,601,506,521,534,609,514,522,530,610,515,523,528,611,513,524,529,510,608,525,533,511,606,526,531,607,512,527,532,542,540,541,545,543,544,548,546,550,551,549,547,670,668,669,671 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#bef86252e34aac6c2a18a1e8b323957fca09c4d4a3c476c0116e0c729e633257, 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 20:32:06 · history