Equation 677 Database

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Magma 60a37ceb2455…

magma 60a37ceb2455
Size
705
Isomorphism class hash
60a37ceb245565addfc1fbcea1b792ddff8a28fd04d1b35bd91ebe5e5c68d107
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 19:53:32
Display reorder
660,460,465,470,474,154,428,432,155,423,427,440,445,153,450,454,520,525,150,530,536,481,485,151,490,494,501,505,152,510,514,580,585,145,590,596,541,545,146,550,556,570,561,565,144,576,645,640,148,650,656,605,601,149,610,616,625,621,147,630,636,691,701,689,699,468,473,471,472,1,422,426,0,424,425,448,453,2,451,452,528,535,3,531,532,488,493,4,491,492,508,513,5,511,512,588,595,6,591,592,548,555,7,551,552,571,568,575,8,572,655,648,9,651,652,615,608,10,611,612,635,628,11,631,632,692,694,687,685,97,314,253,374,131,98,312,129,254,372,96,313,130,252,373,100,317,127,256,377,101,315,128,257,375,99,316,126,255,376,103,320,122,259,380,104,318,120,260,378,258,102,319,121,379,323,106,125,262,383,321,107,123,263,381,322,105,124,261,382,682,676,666,668,410,184,32,350,74,408,185,72,30,348,409,183,73,31,349,413,180,77,35,353,411,181,75,33,351,412,182,76,34,352,416,190,80,27,356,414,191,78,28,354,29,415,189,79,355,186,419,83,26,359,187,417,81,24,357,188,418,82,25,358,670,674,672,684,464,461,467,475,14,431,429,12,433,435,444,441,13,447,455,524,521,17,527,537,484,480,15,487,495,504,500,16,507,515,584,581,20,587,597,544,540,18,547,557,567,564,560,19,577,641,644,23,647,657,600,604,21,607,617,620,624,22,627,637,702,700,693,698,476,477,478,479,179,436,437,177,438,439,456,457,178,458,459,534,533,175,538,539,496,497,176,498,499,516,517,174,518,519,594,593,170,598,599,554,553,168,558,559,578,574,573,169,579,653,654,173,658,659,613,614,171,618,619,633,634,172,638,639,703,704,695,686,466,462,469,463,167,420,421,165,434,430,446,442,166,449,443,526,522,163,529,523,486,482,164,489,483,506,502,162,509,503,586,582,158,589,583,546,542,156,549,543,569,566,562,157,563,642,646,161,649,643,602,606,159,609,603,622,626,160,629,623,690,696,697,688,119,286,326,95,273,117,287,274,324,93,118,285,275,325,94,115,282,272,329,91,116,283,270,327,92,114,284,271,328,90,110,277,264,332,86,108,278,265,330,84,331,109,276,266,85,280,113,267,335,89,281,111,268,333,87,279,112,269,334,88,667,671,679,680,56,362,137,338,251,54,360,249,135,336,55,361,250,136,337,59,365,247,133,341,57,363,248,134,339,58,364,246,132,340,51,368,242,143,344,52,366,240,141,342,142,53,367,241,343,371,50,245,139,347,369,48,243,140,345,370,49,244,138,346,664,673,675,669,398,196,36,292,224,396,197,222,37,293,397,195,223,38,291,401,192,227,39,288,399,193,225,40,289,400,194,226,41,290,404,202,219,42,298,402,203,220,43,299,44,403,201,221,297,198,407,218,45,294,199,405,216,46,295,200,406,217,47,296,677,661,665,681,302,233,386,214,67,300,231,68,384,215,301,232,66,385,213,305,229,70,389,210,303,230,71,387,211,304,228,69,388,212,308,239,65,392,205,306,237,63,390,206,391,307,238,64,204,235,311,61,395,208,236,309,62,393,209,234,310,60,394,207,678,683,662,663 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#b307f9e79abd0b0dc3c5454ee1dbc0a12bcd3b395b4c4aa55143605b1deda3bc, 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 19:53:33 · history