Equation 677 Database

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Magma 20db9f189f44…

magma 20db9f189f44
Size
705
Isomorphism class hash
20db9f189f4428b4a416f8485d5d5fdd9b4ef60192afc1ed4d33b10952661d23
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 16:38:21
Display reorder
660,130,545,346,83,143,347,546,131,84,144,132,547,82,142,348,544,133,349,86,146,542,134,350,87,147,543,135,351,85,145,352,136,89,536,149,353,137,90,537,150,354,138,88,538,148,139,355,92,539,152,140,356,93,540,153,141,357,91,541,151,669,672,666,671,252,581,391,192,108,392,582,250,190,106,251,583,191,107,393,580,255,390,195,111,578,253,388,193,109,579,254,389,194,110,382,258,198,572,114,383,256,196,573,112,384,257,197,574,113,261,385,201,575,117,259,386,199,576,115,260,387,200,577,116,689,691,687,686,487,427,463,50,511,464,428,488,51,512,489,429,49,513,465,426,486,462,46,510,424,484,460,47,508,425,485,461,48,509,454,478,56,418,502,455,479,57,419,503,456,480,55,420,504,481,457,52,421,505,482,458,53,422,506,483,459,54,423,507,664,667,668,665,44,271,211,23,533,212,272,45,21,534,43,273,22,535,213,270,40,210,19,532,268,41,208,20,530,269,42,209,18,531,202,35,14,262,524,203,36,12,263,525,204,34,13,264,526,38,205,17,265,527,39,206,15,266,528,37,207,16,267,529,673,675,679,677,221,593,379,3,403,380,594,222,4,404,220,595,5,405,381,592,224,378,2,402,590,225,376,1,400,591,223,377,0,401,370,219,9,584,394,371,217,10,585,395,372,218,11,586,396,215,373,8,587,397,216,374,6,588,398,214,375,7,589,399,670,662,663,661,557,439,367,161,101,368,440,558,162,102,559,441,160,100,369,438,556,366,164,104,436,554,364,165,105,437,555,365,163,103,358,548,159,430,99,359,549,157,431,97,360,550,158,432,98,551,361,155,433,95,552,362,156,434,96,553,363,154,435,94,695,698,693,694,523,24,617,64,651,655,654,653,65,652,656,657,66,659,658,32,522,616,67,648,33,520,614,68,649,31,521,615,69,650,608,514,62,27,643,609,515,63,25,644,610,516,61,26,642,517,611,58,30,646,518,612,59,28,647,519,613,60,29,645,701,703,702,704,627,173,451,237,569,452,174,628,235,570,629,172,236,571,453,176,626,450,233,568,177,624,448,234,566,175,625,449,232,567,442,618,228,171,560,443,619,226,169,561,444,620,227,170,562,621,445,231,167,563,622,446,229,168,564,623,447,230,166,565,697,700,699,696,499,475,128,81,337,129,476,500,79,338,501,477,80,339,127,474,498,124,77,336,472,496,125,78,334,473,497,126,76,335,119,490,72,466,343,120,491,70,467,344,118,492,71,468,345,493,122,75,469,342,494,123,73,470,340,495,121,74,471,341,676,678,684,682,605,639,245,188,415,246,640,606,189,416,607,641,187,417,244,638,604,248,184,414,636,602,249,185,412,637,603,247,186,413,243,596,179,630,406,241,597,180,631,407,242,598,178,632,408,599,239,182,633,409,600,240,183,634,410,601,238,181,635,411,683,681,674,680,287,315,326,274,303,327,313,288,275,301,286,314,276,302,325,311,290,322,277,299,312,291,323,278,300,310,289,324,279,298,332,293,280,321,309,333,294,281,319,307,331,292,282,320,308,296,328,283,317,305,297,329,284,318,306,295,330,285,316,304,690,688,692,685 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#37e131d0061e11ac6a08c1b5043c4a4bd1e23715ce44e1796d2c3958c15ae4cf, 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 16:38:23 · history