Equation 677 Database

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Magma 888a84e1902e…

magma 888a84e1902e
Size
705
Isomorphism class hash
888a84e1902eda6837f8a493131b4f1012c1b41df2ccafbd4fada7f7be84491e
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 19:54:20
Display reorder
660,495,39,487,493,486,515,40,506,507,513,535,41,526,527,533,38,475,466,467,473,36,433,428,429,432,37,455,446,447,453,45,615,606,607,613,46,635,626,627,633,47,655,646,647,653,595,44,586,587,593,547,555,42,546,553,575,43,566,567,573,686,700,696,688,491,85,494,488,483,511,86,503,514,508,531,84,523,534,528,88,471,463,474,468,89,438,437,439,425,87,451,443,454,448,91,611,603,614,608,92,631,623,634,628,90,651,643,654,648,591,94,583,594,588,554,551,95,543,548,571,93,563,574,568,685,692,689,691,243,69,351,279,399,244,70,400,352,280,245,71,401,353,281,68,242,398,350,278,66,240,396,348,276,67,241,397,349,277,60,249,405,357,285,61,250,406,358,286,62,251,407,359,287,248,63,404,356,284,354,246,64,402,282,247,65,403,355,283,661,675,663,669,169,163,184,204,192,170,164,193,185,205,168,162,194,183,206,166,172,195,180,207,167,173,196,181,208,165,171,197,182,209,161,175,198,190,210,159,176,199,191,211,160,174,200,189,212,178,157,201,186,213,187,179,158,202,214,177,156,203,188,215,673,680,672,676,489,123,484,496,485,509,124,505,504,516,529,125,525,524,536,122,469,465,464,476,120,426,424,423,427,121,449,445,444,456,129,609,605,604,616,130,629,625,624,636,131,649,645,644,656,589,128,585,584,596,544,549,126,545,556,569,127,565,564,576,701,702,699,703,497,12,499,492,498,517,13,518,519,512,538,14,537,539,532,15,477,478,479,472,16,420,421,422,431,17,458,457,459,452,18,617,618,619,612,19,638,637,639,632,20,658,657,659,652,598,21,597,599,592,559,558,22,557,552,577,23,578,579,572,697,690,694,687,481,7,482,490,480,500,8,501,502,510,520,6,521,522,530,10,461,460,462,470,11,435,434,436,430,9,441,440,442,450,5,601,600,602,610,3,621,620,622,630,4,641,640,642,650,580,0,581,582,590,542,540,2,541,550,560,1,561,562,570,695,704,693,698,140,103,147,108,387,138,104,388,148,109,139,102,389,149,110,106,143,386,146,111,107,141,384,144,112,105,142,385,145,113,101,135,393,153,114,99,136,394,154,115,100,137,395,155,116,134,97,392,152,117,150,132,98,390,118,133,96,391,151,119,681,674,667,679,375,48,411,264,252,376,49,253,412,265,377,50,254,413,266,51,374,255,410,267,52,372,256,408,268,53,373,257,409,269,54,381,258,417,270,55,382,259,418,271,56,383,260,419,272,380,57,261,416,273,414,378,58,262,274,379,59,263,415,275,671,678,684,677,313,75,327,228,225,314,76,226,328,229,312,77,227,329,230,74,316,224,326,231,72,317,222,324,232,73,315,223,325,233,81,319,216,333,234,82,320,217,334,235,83,318,218,335,236,322,80,219,332,237,330,323,78,220,238,321,79,221,331,239,683,682,662,665,363,28,339,303,289,364,29,290,340,304,365,27,288,341,305,24,362,292,338,302,25,360,293,336,300,26,361,291,337,301,34,369,295,345,309,35,370,296,346,310,33,371,294,347,311,368,30,298,344,308,342,366,31,299,306,367,32,297,343,307,670,668,664,666 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#b356224f433e80b1c4ac338e7aaea2066ee34f4a7233e2d09dbcc6e7070accf0, 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 19:54:21 · history