Equation 677 Database

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Magma 3a989bc9d29d…

magma 3a989bc9d29d
Size
705
Isomorphism class hash
3a989bc9d29dc1c901d6edaede21d1d86fa6b238d6fa210458333f44aba12542
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 15:51:29
Display reorder
660,33,35,34,31,32,30,26,24,25,29,27,28,547,548,546,550,551,549,545,543,544,541,542,540,589,590,588,592,593,591,595,596,594,598,599,597,244,245,243,240,241,242,250,251,249,246,247,248,184,185,183,180,181,182,190,191,189,186,187,188,682,702,691,701,511,510,512,513,514,515,508,509,507,504,505,506,539,537,538,535,536,534,530,528,529,533,531,532,173,171,172,169,170,168,179,177,178,175,176,174,46,47,45,42,43,44,37,38,36,40,41,39,488,486,487,491,489,490,483,484,485,482,480,481,681,703,700,692,641,640,639,636,637,638,646,647,645,642,643,644,564,565,566,567,568,569,570,571,572,573,574,575,273,274,275,272,270,271,264,265,266,267,268,269,69,70,71,68,66,67,60,61,62,63,64,65,621,622,623,620,618,619,612,613,614,615,616,617,663,685,674,673,603,605,604,601,602,600,611,609,610,607,608,606,256,257,255,252,253,254,262,263,261,258,259,260,576,577,578,579,580,581,582,583,584,585,586,587,235,236,234,238,239,237,233,231,232,229,230,228,561,562,563,560,558,559,552,553,554,555,556,557,664,683,668,669,453,455,454,451,452,450,446,444,445,449,447,448,218,216,217,221,219,220,224,222,223,227,225,226,401,399,400,397,398,396,407,405,406,403,404,402,164,162,163,167,165,166,159,160,161,158,156,157,431,429,430,427,428,426,422,420,421,425,423,424,679,704,697,693,353,352,351,348,349,350,358,359,357,354,355,356,129,130,131,128,126,127,120,121,122,123,124,125,378,379,380,381,382,383,376,377,375,372,373,374,74,72,73,77,75,76,80,78,79,83,81,82,145,146,144,148,149,147,151,152,150,154,155,153,680,696,698,694,85,84,86,87,88,89,90,91,92,93,94,95,633,634,635,632,630,631,624,625,626,627,628,629,280,281,279,276,277,278,286,287,285,282,283,284,648,649,650,651,652,653,654,655,656,657,658,659,9,10,11,8,6,7,1,0,2,3,4,5,689,695,699,690,334,333,335,332,330,331,324,325,326,327,328,329,295,296,294,298,299,297,293,291,292,289,290,288,307,308,306,310,311,309,305,303,304,301,302,300,319,320,318,322,323,321,317,315,316,313,314,312,57,58,59,56,54,55,48,49,50,51,52,53,666,678,677,676,496,495,497,494,492,493,501,502,503,500,498,499,475,476,474,478,479,477,473,471,472,469,470,468,17,15,16,13,14,12,23,21,22,19,20,18,193,194,192,196,197,195,199,200,198,202,203,201,516,517,518,519,520,521,522,523,524,525,526,527,662,687,675,671,435,437,436,433,434,432,443,441,442,439,440,438,410,408,409,413,411,412,416,414,415,419,417,418,456,457,458,459,460,461,462,463,464,465,466,467,207,208,209,206,204,205,213,214,215,212,210,211,384,385,386,387,388,389,390,391,392,393,394,395,661,684,672,670,110,109,108,112,113,111,115,116,114,118,119,117,137,135,136,133,134,132,143,141,142,139,140,138,365,363,364,361,362,360,371,369,370,367,368,366,96,97,98,99,100,101,102,103,104,105,106,107,341,339,340,337,338,336,347,345,346,343,344,342,665,686,667,688 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {62} 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 15:51:33 · history