Equation 677 Database

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Magma 883a28a17918…

magma 883a28a17918
Size
705
Isomorphism class hash
883a28a179187247eca47d4afc3cc73802edf8a3c19e9ad4e7736c46d451370d
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 21:57:46
Display reorder
660,119,234,36,228,513,117,235,37,229,514,118,233,38,227,512,237,115,39,231,509,238,40,232,510,116,236,114,41,230,511,110,42,240,226,519,108,43,241,224,520,109,44,239,225,518,45,113,243,222,515,223,46,111,244,516,47,112,242,221,517,672,668,670,662,8,269,284,525,573,6,270,285,526,574,7,271,286,524,572,272,11,283,521,569,273,281,522,570,9,274,10,282,523,571,3,290,275,531,579,4,291,276,532,580,5,292,277,530,578,289,2,278,527,575,528,287,1,279,576,288,0,280,529,577,686,689,688,690,155,465,261,441,597,153,466,262,442,598,154,464,260,440,596,461,151,257,437,593,462,258,438,594,152,463,150,259,439,595,146,267,471,447,603,144,268,472,448,604,145,266,470,446,602,263,149,467,443,599,444,264,147,468,600,265,148,469,445,601,665,671,661,667,295,214,122,207,489,293,212,120,208,490,294,213,121,206,488,210,298,125,203,485,211,123,204,486,296,209,297,124,205,487,301,128,220,198,495,299,126,218,199,496,300,127,219,197,494,131,304,216,201,491,202,129,302,217,492,130,303,215,200,493,683,679,677,673,92,21,369,453,537,90,22,370,454,538,91,23,368,452,536,20,95,365,449,533,18,366,450,534,93,19,94,367,451,535,87,375,12,459,543,88,376,13,460,544,89,374,14,458,542,371,86,15,455,539,456,372,84,16,540,373,85,17,457,541,666,669,663,664,52,250,477,405,561,53,248,478,406,562,51,249,476,404,560,246,48,473,401,557,247,474,402,558,49,245,50,475,403,559,58,483,256,411,567,59,484,254,412,568,57,482,255,410,566,479,54,252,407,563,408,480,55,253,564,481,56,251,409,565,694,697,695,693,194,609,355,180,364,195,635,634,633,632,196,608,356,184,363,605,193,358,181,360,606,359,182,361,191,607,192,357,183,362,185,652,655,654,653,186,656,659,658,657,187,648,651,650,649,636,188,639,638,637,642,640,189,643,641,645,190,647,646,644,703,701,704,702,79,321,333,311,342,80,322,334,309,340,78,323,335,310,341,320,82,332,307,338,318,330,308,339,83,319,81,331,306,337,77,324,312,629,628,75,325,313,631,630,76,326,314,627,626,327,73,315,305,336,623,328,74,316,622,329,72,317,624,625,699,700,696,698,103,429,585,501,614,104,430,586,502,615,102,428,584,500,613,425,106,581,497,610,426,582,498,611,107,427,105,583,499,612,101,591,435,507,620,99,592,436,508,621,100,590,434,506,619,587,97,431,503,616,504,588,98,432,617,589,96,433,505,618,680,684,682,676,350,549,393,417,177,351,550,394,418,178,349,548,392,416,179,545,353,389,413,176,546,390,414,174,354,547,352,391,415,175,348,399,555,423,168,346,400,556,424,169,347,398,554,422,170,395,344,551,419,171,420,396,345,552,172,397,343,553,421,173,675,678,674,681,70,35,385,140,164,71,33,383,138,162,69,34,384,139,163,31,66,388,143,167,32,386,141,165,67,30,68,387,142,166,61,380,26,135,159,62,381,24,136,160,60,382,25,137,161,379,64,29,134,158,132,377,65,27,156,378,63,28,133,157,685,687,691,692 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#fdf5f382e471d95c048f9fa2e9b8340aa5eb614276b1c155a6fb7129b8435eb8, 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 21:57:46 · history