Equation 677 Database

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Magma 32c07d67adfe…

magma 32c07d67adfe
Size
705
Isomorphism class hash
32c07d67adfe90acd3c9baab5c05e65603db5c5ee6547390bfd8af17dcebe184
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 19:56:01
Display reorder
660,653,30,652,649,641,613,31,612,609,600,633,32,632,629,620,33,573,572,569,561,34,593,592,589,581,35,553,552,549,540,473,28,472,469,461,433,29,432,429,421,453,27,452,449,440,24,533,532,529,520,25,493,492,489,481,26,513,512,509,501,689,701,694,698,640,154,657,648,651,601,155,617,608,611,621,153,637,628,631,150,560,577,568,571,151,580,597,588,591,152,541,557,548,551,460,145,477,468,471,422,146,435,428,431,441,144,457,448,451,148,521,537,528,531,149,480,497,488,491,147,500,517,508,511,702,693,690,696,167,81,6,407,215,165,82,7,405,213,166,83,8,406,214,80,163,9,403,211,78,164,10,404,212,79,162,11,402,210,158,72,4,398,206,156,73,5,396,204,157,74,3,397,205,75,161,1,401,209,76,159,0,399,207,77,160,2,400,208,680,678,666,676,88,17,347,117,131,89,15,345,118,129,87,16,346,119,130,13,84,343,116,127,14,85,344,114,128,12,86,342,115,126,94,23,338,108,122,95,21,336,109,120,93,22,337,110,121,19,90,341,111,125,20,91,339,112,123,18,92,340,113,124,662,670,671,673,643,222,654,656,642,603,223,614,616,602,623,224,634,636,622,225,563,574,576,562,226,583,594,596,582,227,543,554,556,542,463,220,474,476,462,423,221,438,439,437,443,219,454,456,442,216,523,534,536,522,217,483,494,496,482,218,503,514,516,502,691,686,700,687,659,101,658,655,646,619,99,618,615,606,639,100,638,635,626,97,579,578,575,566,98,599,598,595,586,96,559,558,555,546,479,107,478,475,466,420,105,436,434,426,459,106,458,455,446,103,539,538,535,526,104,499,498,495,486,102,519,518,515,506,697,704,699,688,647,60,644,645,650,607,61,604,605,610,627,62,624,625,630,63,567,564,565,570,64,587,584,585,590,65,547,544,545,550,467,66,464,465,470,427,67,424,425,430,447,68,444,445,450,69,527,524,525,530,70,487,484,485,490,71,507,504,505,510,695,692,685,703,251,174,323,419,237,249,175,321,417,238,250,176,322,418,239,177,247,319,415,236,178,248,320,416,234,179,246,318,414,235,242,172,314,410,228,240,173,312,408,229,241,171,313,409,230,168,245,317,413,231,169,243,315,411,232,170,244,316,412,233,684,681,661,668,359,198,261,275,335,357,199,262,273,333,358,200,263,274,334,201,355,260,271,331,202,356,258,272,332,203,354,259,270,330,350,196,252,266,326,348,197,253,264,324,349,195,254,265,325,192,353,255,269,329,193,351,256,267,327,194,352,257,268,328,663,669,674,683,383,137,287,311,299,381,135,285,309,297,382,136,286,310,298,133,379,283,307,295,134,380,284,308,296,132,378,282,306,294,374,143,278,302,290,372,141,276,300,288,373,142,277,301,289,139,377,281,305,293,140,375,279,303,291,138,376,280,304,292,667,665,677,664,48,180,395,371,37,49,181,393,369,38,50,182,394,370,36,183,51,391,367,40,184,52,392,368,41,185,53,390,366,39,54,186,386,362,43,55,187,384,360,44,56,188,385,361,42,189,57,389,365,46,190,58,387,363,47,191,59,388,364,45,675,672,682,679 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#b42b2593cdf495fd739236f86f5dbe699df6ba394eb7d6a8f934bf0cd7c90649, 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 19:56:02 · history