Equation 677 Database

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Magma 590a86f20425…

magma 590a86f20425
Size
705
Isomorphism class hash
590a86f204251fa8c6d6ea61fe9003c4998c623242a7914ee06a43cb80b998cf
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 19:15:27
Display reorder
660,453,443,78,442,447,463,462,473,79,467,422,423,434,80,429,516,504,81,503,508,82,524,536,523,528,496,484,83,483,488,564,576,76,563,568,584,596,77,583,588,544,556,75,543,548,636,624,72,623,628,656,644,73,643,648,616,604,74,603,608,701,700,693,686,451,440,113,441,444,460,461,471,111,464,421,420,432,112,426,512,501,109,502,505,110,521,532,522,525,492,480,108,482,485,561,572,119,562,565,581,592,117,582,585,541,552,118,542,545,632,620,115,622,625,652,640,116,642,645,612,600,114,602,605,697,695,690,688,259,21,125,361,218,22,362,260,123,216,360,23,258,124,217,262,20,121,364,221,122,18,263,365,219,261,19,120,363,220,12,257,131,367,224,13,255,129,368,222,14,256,130,366,223,253,15,127,370,227,254,16,128,371,225,252,17,126,369,226,674,669,677,676,325,349,56,103,34,350,104,326,54,35,102,348,324,55,33,328,352,59,106,30,57,353,329,107,31,327,351,58,105,32,355,331,51,101,25,356,332,52,99,26,354,330,53,100,24,334,358,50,97,28,335,359,48,98,29,333,357,49,96,27,681,671,668,673,458,446,282,445,459,466,465,479,283,477,427,428,439,284,437,518,507,285,506,500,286,527,538,526,520,498,487,287,486,481,567,578,280,566,560,587,598,281,586,580,547,558,279,546,540,638,627,276,626,621,658,647,277,646,641,618,607,278,606,601,685,702,699,691,455,456,62,457,452,476,478,475,60,472,436,438,435,61,433,519,514,65,515,513,63,534,539,535,533,499,494,64,495,493,574,579,68,575,573,594,599,66,595,593,554,559,67,555,553,639,634,71,635,633,659,654,69,655,653,619,614,70,615,613,692,698,703,687,449,450,322,448,454,470,468,469,323,474,430,431,424,321,425,510,511,318,509,517,319,531,530,529,537,490,491,320,489,497,571,570,313,569,577,591,590,314,589,597,551,550,312,549,557,630,631,316,629,637,650,651,317,649,657,610,611,315,609,617,694,696,704,689,132,240,267,237,409,241,238,133,268,410,239,242,134,269,408,135,243,266,236,412,264,244,136,234,413,137,245,265,235,411,246,138,273,228,415,247,139,274,229,416,248,140,275,230,414,141,249,272,231,418,142,250,270,232,419,143,251,271,233,417,661,683,662,678,397,38,176,301,94,36,302,398,174,95,300,37,396,175,93,400,41,179,304,90,177,39,401,305,91,399,40,178,303,92,44,403,171,307,85,42,404,172,308,86,43,402,173,306,84,406,47,170,310,88,407,45,168,311,89,405,46,169,309,87,664,666,682,672,373,214,157,195,385,215,196,374,158,386,197,213,372,156,384,376,210,160,194,388,161,211,377,192,389,375,212,159,193,387,205,379,163,201,391,206,380,164,202,392,204,378,162,203,390,382,208,166,200,394,383,209,167,198,395,381,207,165,199,393,667,679,675,665,337,2,153,181,289,1,182,338,154,290,180,0,336,155,288,340,5,152,184,292,150,3,341,185,293,339,4,151,183,291,8,343,144,187,295,6,344,145,188,296,7,342,146,186,294,346,11,147,190,298,347,9,148,191,299,345,10,149,189,297,684,663,670,680 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#966159413732cc97ab9cbe48ea19b17c045c0e7dae7d4f88fdd62e86aa428734, 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 19:15:28 · history