Equation 677 Database

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Magma 3a03b9e460b8…

magma 3a03b9e460b8
Size
705
Isomorphism class hash
3a03b9e460b86e97e7acec537f559304db5154ac0e74871bf7ac89e99a88450f
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 21:17:27
Display reorder
660,296,556,558,555,543,294,576,578,575,563,295,596,595,598,583,299,616,618,615,603,297,636,638,635,623,298,656,658,655,643,291,516,518,515,501,292,536,538,535,521,293,496,498,495,480,290,427,429,426,421,288,454,456,453,440,289,474,476,473,460,691,694,687,690,129,545,559,546,544,130,565,579,566,564,131,585,586,599,584,128,605,619,606,604,126,625,639,626,624,127,645,659,646,644,120,505,519,506,504,121,525,539,526,524,122,485,499,486,484,123,431,437,423,422,124,444,457,445,443,125,464,477,465,463,698,702,686,699,107,235,211,414,6,105,236,212,415,7,106,234,416,210,8,103,238,214,417,9,104,239,215,418,10,102,237,213,419,11,98,233,209,412,4,96,231,207,413,5,97,232,208,411,3,101,229,205,408,1,99,230,206,409,0,100,228,204,410,2,664,661,670,682,12,72,184,342,390,17,73,185,343,391,13,74,344,183,392,21,75,180,345,393,23,76,181,346,394,18,77,182,347,395,14,78,190,340,388,15,79,191,341,389,16,80,189,339,387,19,81,186,336,384,20,82,187,337,385,22,83,188,338,386,662,665,678,671,217,547,554,548,549,218,567,574,568,569,216,587,588,594,589,220,607,614,608,609,221,627,634,628,629,219,647,654,648,649,223,507,514,508,509,224,527,534,528,529,222,487,494,488,489,226,424,425,432,433,227,446,452,447,448,225,466,472,467,468,689,704,695,692,281,550,540,551,553,279,570,561,571,573,280,590,591,581,593,277,610,601,611,613,278,630,620,631,633,276,650,640,651,653,287,510,502,511,513,285,530,522,531,533,286,490,482,491,493,283,434,430,435,436,284,449,441,450,451,282,469,461,470,471,693,696,703,688,147,541,552,557,542,148,560,572,577,562,149,580,597,592,582,146,600,612,617,602,144,621,632,637,622,145,641,652,657,642,153,500,512,517,503,154,520,532,537,523,155,481,492,497,483,152,439,438,428,420,150,459,458,455,442,151,479,478,475,462,700,685,701,697,116,366,378,64,318,114,367,379,65,319,115,368,63,380,320,119,369,381,60,321,117,370,382,61,322,118,371,383,62,323,111,364,376,70,316,112,365,377,71,317,113,363,375,69,315,110,360,372,66,312,108,361,373,67,313,109,362,374,68,314,675,677,668,680,84,268,251,173,262,85,269,249,171,263,86,267,172,250,261,87,264,247,169,258,88,265,248,170,259,89,266,246,168,260,90,274,242,179,253,91,275,240,177,254,92,273,241,178,252,93,270,245,175,256,94,271,243,176,257,95,272,244,174,255,673,684,667,681,201,27,38,354,402,202,28,36,355,403,203,29,356,37,404,200,26,41,357,405,198,24,39,358,406,199,25,40,359,407,192,33,44,352,400,193,34,42,353,401,194,35,43,351,399,195,32,47,348,396,196,30,45,349,397,197,31,46,350,398,683,674,679,672,157,330,306,143,54,158,331,307,141,55,156,332,142,308,56,160,333,309,139,57,161,334,310,140,58,159,335,311,138,59,163,328,304,134,52,164,329,305,132,53,162,327,303,133,51,166,324,300,137,48,167,325,301,135,49,165,326,302,136,50,669,666,676,663 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#e3fb677801a83abf4523d8c5dab7d3c82647015c862300302a3edde7221f68e9, 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 21:17:28 · history