Equation 677 Database

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Magma 9f1e146bef27…

magma 9f1e146bef27
Size
705
Isomorphism class hash
9f1e146bef27b9782a73214c7bc2265ada3fe9b047d42ef9d3c1460083f38cdb
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 16:23:52
Display reorder
660,541,38,554,552,557,561,36,574,572,577,581,37,594,592,597,601,41,614,612,617,39,621,634,632,637,652,641,40,654,657,514,500,44,512,517,534,520,42,532,537,494,481,43,492,497,422,434,47,432,437,443,451,45,456,457,462,474,46,472,477,690,701,702,692,545,102,551,559,558,565,103,571,579,578,585,104,591,598,599,605,105,611,619,618,106,625,631,639,638,658,645,107,651,659,511,505,100,519,518,531,525,101,539,538,491,485,99,499,498,425,431,96,439,438,445,450,97,459,458,465,471,98,478,479,687,695,685,686,373,145,409,176,408,375,146,411,174,410,376,144,413,175,412,379,148,415,179,414,149,381,417,177,416,178,382,147,419,418,404,369,151,171,405,406,370,152,172,407,403,367,150,173,402,361,396,154,170,397,363,398,155,168,399,364,400,153,169,401,670,683,684,679,306,2,199,372,354,307,1,200,374,355,308,0,198,377,356,309,5,202,378,357,3,310,203,380,358,383,311,4,201,359,197,304,8,368,352,195,305,6,371,353,196,303,7,366,351,300,193,11,360,348,301,194,9,362,349,302,192,10,365,350,678,676,667,672,544,86,555,546,550,564,84,575,566,570,584,85,595,586,590,604,89,615,606,610,87,624,635,626,630,646,644,88,655,650,515,504,92,506,510,535,524,90,526,530,495,484,91,486,490,424,435,95,426,430,452,454,93,446,449,464,475,94,466,470,689,698,696,693,548,34,556,543,547,568,35,576,563,567,588,33,596,583,587,608,30,616,603,607,31,628,636,623,627,643,648,32,656,647,516,508,25,503,507,536,528,26,523,527,496,488,24,483,487,428,436,28,423,427,453,455,29,444,447,468,476,27,463,467,699,694,697,688,549,207,542,553,540,569,208,562,573,560,589,209,582,593,580,609,206,602,613,600,204,629,622,633,620,653,649,205,642,640,502,509,213,513,501,522,529,214,533,521,482,489,215,493,480,429,420,212,433,421,448,442,210,441,440,469,461,211,473,460,691,703,704,700,76,66,294,270,342,77,67,295,271,343,75,68,296,272,344,72,69,297,273,345,70,73,298,274,346,275,74,71,299,347,292,82,64,268,340,293,83,65,269,341,291,81,63,267,339,78,288,60,264,336,79,289,61,265,337,80,290,62,266,338,665,675,669,680,282,56,181,161,390,283,54,182,159,391,284,55,180,160,392,285,59,184,157,393,57,286,185,158,394,156,287,58,183,395,187,280,51,167,388,188,281,52,165,389,186,279,53,166,387,276,190,50,163,384,277,191,48,164,385,278,189,49,162,386,668,682,677,666,330,19,135,234,118,331,20,136,235,119,332,18,137,236,117,333,22,134,237,114,23,334,132,238,115,239,335,21,133,116,141,328,17,232,109,142,329,15,233,110,143,327,16,231,108,324,140,13,228,112,325,138,14,229,113,326,139,12,230,111,661,681,671,674,258,124,246,318,216,259,125,247,319,217,260,123,248,320,218,261,120,249,321,219,121,262,250,322,220,323,263,122,251,221,244,256,130,316,222,245,257,131,317,223,243,255,129,315,224,252,240,126,312,225,253,241,127,313,226,254,242,128,314,227,673,662,663,664 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#2fbfbc696f8770de67b632f9354275e3bbc4952318d0e644426634c23ae4ab08, 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 16:23:54 · history