Equation 677 Database

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Magma f3765a905237…

magma f3765a905237
Size
705
Isomorphism class hash
f3765a9052379fac94099dc34633afbc98676d9a6df551394f9faa54f6680255
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 15:53:40
Display reorder
660,344,343,342,346,347,345,341,339,340,337,338,336,370,371,369,366,367,368,361,362,360,364,365,363,168,169,170,171,172,173,174,175,176,177,178,179,481,482,480,484,485,483,487,488,486,490,491,489,536,534,535,539,537,538,531,532,533,530,528,529,682,702,690,701,372,374,373,377,375,376,380,378,379,383,381,382,355,356,354,358,359,357,353,351,352,349,350,348,478,479,477,474,475,476,469,470,468,472,473,471,455,453,454,451,452,450,446,444,445,449,447,448,420,421,422,423,424,425,426,427,428,429,430,431,681,703,700,692,79,78,80,81,82,83,76,77,75,72,73,74,553,554,552,556,557,555,559,560,558,562,563,561,576,577,578,579,580,581,582,583,584,585,586,587,132,133,134,135,136,137,138,139,140,141,142,143,31,32,30,34,35,33,29,27,28,25,26,24,663,685,671,672,542,541,540,544,545,543,547,548,546,550,551,549,327,328,329,326,324,325,333,334,335,332,330,331,156,157,158,159,160,161,162,163,164,165,166,167,493,494,492,496,497,495,499,500,498,502,503,501,519,520,521,518,516,517,525,526,527,524,522,523,664,683,668,674,7,6,8,9,10,11,4,5,3,1,0,2,515,513,514,511,512,510,506,504,505,509,507,508,105,106,107,104,102,103,96,97,98,99,100,101,620,618,619,623,621,622,615,616,617,614,612,613,236,234,235,239,237,238,231,232,233,230,228,229,679,704,697,693,627,629,628,625,626,624,635,633,634,631,632,630,20,18,19,23,21,22,15,16,17,14,12,13,656,654,655,659,657,658,651,652,653,650,648,649,241,242,240,244,245,243,247,248,246,250,251,249,110,108,109,113,111,112,116,114,115,119,117,118,680,696,698,694,127,126,128,129,130,131,124,125,123,120,121,122,591,592,593,590,588,589,597,598,599,596,594,595,571,572,570,574,575,573,569,567,568,565,566,564,153,154,155,152,150,151,144,145,146,147,148,149,69,70,71,68,66,67,60,61,62,63,64,65,689,695,699,691,285,287,286,283,284,282,278,276,277,281,279,280,298,299,297,294,295,296,289,290,288,292,293,291,310,311,309,306,307,308,301,302,300,304,305,303,323,321,322,319,320,318,314,312,313,317,315,316,43,44,42,46,47,45,41,39,40,37,38,36,666,678,667,677,456,458,457,461,459,460,464,462,463,467,465,466,435,436,437,434,432,433,441,442,443,440,438,439,409,410,408,412,413,411,415,416,414,418,419,417,390,391,392,393,394,395,388,389,387,384,385,386,53,51,52,49,50,48,59,57,58,55,56,54,662,687,669,675,396,398,397,401,399,400,404,402,403,407,405,406,607,608,606,610,611,609,605,603,604,601,602,600,224,222,223,227,225,226,219,220,221,218,216,217,191,189,190,187,188,186,182,180,181,185,183,184,90,91,92,93,94,95,88,89,87,84,85,86,661,684,673,676,195,197,196,193,194,192,203,201,202,199,200,198,206,204,205,209,207,208,212,210,211,215,213,214,252,253,254,255,256,257,258,259,260,261,262,263,265,266,264,268,269,267,271,272,270,274,275,273,643,644,642,646,647,645,641,639,640,637,638,636,665,686,670,688 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {64} 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 15:53:41 · history