Equation 677 Database

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Magma 9e8fa288ee24…

magma 9e8fa288ee24
Size
705
Isomorphism class hash
9e8fa288ee247c52c27b818d1288f45780f0808b912ae998196d6802f80afd9f
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 15:50:43
Display reorder
663,279,281,280,277,278,276,287,285,286,283,284,282,498,499,500,501,502,503,496,497,495,492,493,494,535,536,534,538,539,537,533,531,532,529,530,528,24,25,26,27,28,29,30,31,32,33,34,35,337,338,336,340,341,339,343,344,342,346,347,345,660,673,675,670,171,173,172,169,170,168,179,177,178,175,176,174,66,67,68,69,70,71,64,65,63,60,61,62,78,79,80,81,82,83,76,77,75,72,73,74,605,603,604,601,602,600,611,609,610,607,608,606,8,6,7,11,9,10,3,4,5,2,1,0,683,688,687,689,366,368,367,371,369,370,363,364,365,362,360,361,227,225,226,223,224,222,218,216,217,221,219,220,239,237,238,235,236,234,230,228,229,233,231,232,557,555,556,553,554,552,563,561,562,559,560,558,309,310,311,308,306,307,300,301,302,303,304,305,662,672,674,671,419,418,417,414,415,416,409,410,408,412,413,411,621,622,623,620,618,619,612,613,614,615,616,617,14,12,13,17,15,16,20,18,19,23,21,22,628,629,627,624,625,626,634,635,633,630,631,632,188,186,187,191,189,190,183,184,185,182,180,181,667,679,676,681,211,210,212,213,214,215,208,209,207,204,205,206,103,104,102,106,107,105,101,99,100,97,98,96,647,645,646,643,644,642,638,636,637,641,639,640,200,198,199,203,201,202,195,196,197,194,192,193,421,422,420,424,425,423,427,428,426,430,431,429,661,666,665,668,289,288,290,291,292,293,294,295,296,297,298,299,540,541,542,543,544,545,546,547,548,549,550,551,357,358,359,356,354,355,348,349,350,351,352,353,515,513,514,511,512,510,506,504,505,509,507,508,54,55,56,57,58,59,52,53,51,48,49,50,691,700,701,699,449,448,447,444,445,446,454,455,453,450,451,452,475,476,474,478,479,477,473,471,472,469,470,468,463,464,462,466,467,465,461,459,460,457,458,456,486,487,488,489,490,491,484,485,483,480,481,482,443,441,442,439,440,438,434,432,433,437,435,436,698,703,704,702,115,114,116,117,118,119,112,113,111,108,109,110,649,650,648,652,653,651,655,656,654,658,659,657,252,253,254,255,256,257,258,259,260,261,262,263,248,246,247,251,249,250,243,244,245,242,240,241,137,135,136,133,134,132,143,141,142,139,140,138,690,696,695,697,517,516,518,519,520,521,522,523,524,525,526,527,585,586,587,584,582,583,576,577,578,579,580,581,330,331,332,333,334,335,328,329,327,324,325,326,270,271,272,273,274,275,268,269,267,264,265,266,388,389,387,384,385,386,394,395,393,390,391,392,669,685,686,684,396,398,397,401,399,400,404,402,403,407,405,406,150,151,152,153,154,155,148,149,147,144,145,146,591,592,593,590,588,589,597,598,599,596,594,595,164,162,163,167,165,166,159,160,161,158,156,157,44,42,43,47,45,46,39,40,41,38,36,37,664,678,677,682,567,569,568,565,566,564,575,573,574,571,572,570,127,128,126,130,131,129,125,123,124,121,122,120,92,90,91,95,93,94,87,88,89,86,84,85,322,323,321,318,319,320,313,314,312,316,317,315,382,383,381,378,379,380,373,374,372,376,377,375,680,693,694,692 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 = {61} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 15:50:44 · history