Equation 677 Database

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Magma 4e70ab5750a8…

magma 4e70ab5750a8
Size
705
Isomorphism class hash
4e70ab5750a89acc69a51c6a81ac0a6c5d5f6ab9d3cfdbd2875e8862f3b88c77
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 16:48:57
Display reorder
660,558,271,42,426,188,559,272,43,427,186,557,270,41,425,187,267,554,45,422,184,46,555,268,423,185,269,556,44,424,183,549,262,40,417,179,550,263,38,418,177,548,261,39,416,178,265,552,36,420,182,266,553,37,421,180,264,551,35,419,181,661,666,670,668,353,132,113,64,53,351,133,111,62,54,352,134,112,63,55,131,356,116,60,56,114,354,129,61,57,130,355,115,59,58,348,138,108,70,51,349,139,109,68,52,350,140,110,69,50,137,347,107,66,47,135,345,105,67,48,136,346,106,65,49,689,690,688,685,23,641,292,606,206,24,642,293,607,204,25,640,291,605,205,637,26,295,602,202,296,27,638,603,203,639,28,294,604,201,29,632,290,597,212,30,633,288,598,210,31,631,289,596,211,635,32,286,600,208,636,33,287,601,209,634,34,285,599,207,671,667,672,664,368,474,123,546,11,366,475,124,547,12,367,473,125,545,13,470,364,126,542,14,127,365,471,543,15,472,363,128,544,16,359,465,121,537,17,357,466,122,538,18,358,464,120,536,19,468,362,117,540,20,469,360,118,541,21,467,361,119,539,22,680,678,676,681,450,510,370,311,582,451,511,371,309,583,449,509,369,310,581,506,446,373,314,578,374,447,507,312,579,508,448,372,313,580,441,501,376,317,573,442,502,377,315,574,440,500,375,316,572,504,444,379,320,576,505,445,380,318,577,503,443,378,319,575,662,669,665,663,190,498,275,522,146,191,499,273,523,144,189,497,274,521,145,494,193,278,518,142,276,194,495,519,143,496,192,277,520,141,196,489,281,513,152,197,490,279,514,150,195,488,280,512,151,492,199,284,516,148,493,200,282,517,149,491,198,283,515,147,696,693,695,697,71,653,96,618,86,658,659,97,656,657,78,652,98,617,85,649,79,95,614,82,93,80,650,615,83,651,81,94,616,84,77,644,102,609,92,75,645,103,610,90,76,643,104,608,91,647,73,101,612,88,648,74,99,613,89,646,72,100,611,87,702,703,704,701,414,6,328,403,387,415,654,329,401,655,413,10,327,402,391,7,410,331,399,388,332,411,8,400,389,9,412,330,398,390,405,4,326,394,385,406,5,324,392,386,404,3,325,393,384,1,408,322,397,381,0,409,323,395,382,2,407,321,396,383,698,699,700,694,486,157,254,165,570,487,158,252,166,571,485,156,253,167,569,153,482,250,168,566,251,483,154,169,567,155,484,249,170,568,477,163,260,171,561,478,164,258,172,562,476,162,259,173,560,159,480,256,174,564,160,481,257,175,565,161,479,255,176,563,673,682,675,677,594,438,344,534,629,595,439,342,535,630,593,437,343,533,628,434,590,340,530,625,341,591,435,531,626,436,592,339,532,627,585,429,335,525,620,586,430,333,526,621,584,428,334,524,619,432,588,338,528,623,433,589,336,529,624,431,587,337,527,622,679,684,674,683,216,229,297,462,237,217,230,298,463,238,218,228,299,461,239,225,215,300,458,240,301,213,226,459,241,227,214,302,460,242,222,235,303,453,243,223,236,304,454,244,224,234,305,452,245,231,221,306,456,246,232,219,307,457,247,233,220,308,455,248,687,692,691,686 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#3f4c16e16e9bd422beeb4e3c1331ed0b07b0ac931af0d47b2d7497fadfe20a6b, M = {60} 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 16:48:58 · history