Equation 677 Database

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Magma 8bf4b1a87782…

magma 8bf4b1a87782
Size
705
Isomorphism class hash
8bf4b1a87782569a2d6b3e4a2e5b109c7492f7b67e403351009b392368fd0536
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 15:18:16
Display reorder
660,553,544,299,557,558,297,573,577,578,564,298,584,593,597,598,613,295,604,617,618,633,296,624,637,638,653,294,644,657,658,513,290,504,517,518,533,288,524,537,538,493,289,484,497,498,293,425,420,427,428,291,452,445,455,456,292,472,465,475,476,696,699,686,689,540,554,157,556,559,158,561,576,579,574,156,594,581,596,599,601,160,614,616,619,620,161,634,636,639,640,159,654,656,659,501,163,514,516,519,520,164,534,536,539,481,162,494,496,499,166,431,437,426,429,167,442,453,454,457,165,462,473,474,477,693,702,692,691,139,402,222,110,103,223,140,108,104,403,224,404,138,109,102,142,225,405,113,106,143,226,406,111,107,141,227,407,112,105,137,220,400,116,101,135,221,401,114,99,136,219,399,115,100,216,133,396,119,97,217,134,397,117,98,218,132,398,118,96,663,664,675,681,378,318,23,256,249,21,379,257,250,319,22,320,380,255,251,381,19,321,252,248,382,20,322,253,246,383,18,323,254,247,376,14,316,262,240,377,12,317,263,241,375,13,315,261,242,17,372,312,258,243,15,373,313,259,244,16,374,314,260,245,672,661,678,666,546,545,31,547,549,32,566,567,569,565,30,585,586,587,589,606,34,605,607,609,626,35,625,627,629,646,33,645,647,649,506,29,505,507,509,526,27,525,527,529,486,28,485,487,489,25,422,421,434,435,26,446,441,447,448,24,466,461,467,468,695,704,700,697,543,542,277,551,541,278,563,571,560,562,276,582,583,591,580,603,280,602,611,600,623,281,622,631,621,643,279,642,651,641,503,283,502,511,500,523,284,522,531,521,483,282,482,491,480,286,433,432,436,430,287,444,443,450,440,285,464,463,470,460,698,701,703,694,555,548,271,550,552,272,575,570,572,568,270,588,595,590,592,615,274,608,610,612,635,275,628,630,632,655,273,648,650,652,515,269,508,510,512,535,267,528,530,532,495,268,488,490,492,265,438,439,423,424,266,459,458,449,451,264,478,479,469,471,688,687,690,685,175,147,93,342,330,94,176,343,331,148,95,149,174,344,332,178,92,146,345,333,179,90,144,346,334,177,91,145,347,335,173,84,153,340,328,171,85,154,341,329,172,86,155,339,327,87,169,152,336,324,88,170,150,337,325,89,168,151,338,326,669,668,667,676,46,210,3,71,58,4,47,69,59,211,5,212,45,70,57,42,2,213,67,54,43,1,214,68,55,44,0,215,66,56,37,9,208,62,49,38,10,209,60,50,36,11,207,61,48,8,40,204,65,52,6,41,205,63,53,7,39,206,64,51,680,684,671,673,414,390,239,127,366,237,415,128,367,391,238,392,416,126,368,417,235,393,130,369,418,236,394,131,370,419,234,395,129,371,412,230,388,125,364,413,228,389,123,365,411,229,387,124,363,233,408,384,121,360,231,409,385,122,361,232,410,386,120,362,683,677,682,679,202,184,78,354,306,79,203,355,307,185,80,183,201,356,308,198,81,180,357,309,199,82,181,358,310,200,83,182,359,311,193,76,190,352,304,194,77,191,353,305,192,75,189,351,303,72,196,186,348,300,73,197,187,349,301,74,195,188,350,302,674,665,662,670 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#11540e60a31227d97822464caf7bd085f23c491501101f6992da34196185b51e, 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 15:18:18 · history