Equation 677 Database

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Magma fca5587772d8…

magma fca5587772d8
Size
705
Isomorphism class hash
fca5587772d879f08a1c58a5b64359ce47ad5a882878bcd5654efd0da97a4a05
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 21:17:01
Display reorder
660,342,329,404,316,333,343,327,334,402,317,344,328,335,403,315,345,325,332,407,312,346,326,330,405,313,347,324,331,406,314,339,348,410,320,307,340,349,408,318,308,341,350,409,319,306,351,338,413,323,310,352,336,411,321,311,353,337,412,322,309,672,664,666,662,481,215,17,493,634,482,213,635,15,494,480,214,633,16,492,484,211,637,13,496,485,212,638,14,497,483,210,636,12,495,632,479,23,221,491,630,477,21,219,489,631,478,22,220,490,475,628,19,217,487,476,629,20,218,488,474,627,18,216,486,688,686,687,692,68,457,92,385,373,66,458,374,90,386,67,456,372,91,384,64,460,376,88,388,65,461,377,89,389,63,459,375,87,387,371,59,83,455,383,369,57,81,453,381,370,58,82,454,382,62,367,86,451,379,60,368,84,452,380,61,366,85,450,378,665,667,663,661,231,622,47,234,397,232,623,398,45,235,233,621,396,46,236,230,625,400,50,237,228,626,401,48,238,229,624,399,49,239,395,222,53,620,240,393,223,51,618,241,394,224,52,619,242,225,391,56,616,243,226,392,54,617,244,227,390,55,615,245,683,677,673,674,541,565,139,553,257,542,566,255,140,554,540,564,256,138,552,544,568,253,142,556,545,569,254,143,557,543,567,252,141,555,248,539,145,563,551,246,537,146,561,549,247,538,144,562,550,535,251,148,559,547,536,249,149,560,548,534,250,147,558,546,670,668,669,671,421,445,263,360,433,422,446,434,261,361,420,444,432,262,362,424,448,436,259,363,425,449,437,260,364,423,447,435,258,365,431,419,269,443,358,429,417,267,441,359,430,418,268,442,357,415,427,265,439,354,416,428,266,440,355,414,426,264,438,356,696,694,698,695,135,44,11,645,613,136,42,614,9,646,137,43,612,10,647,652,653,654,7,655,656,657,658,8,659,649,648,650,6,651,611,133,2,39,643,609,134,1,40,644,610,132,0,41,642,129,607,5,38,639,130,608,3,36,640,131,606,4,37,641,703,702,701,704,589,172,127,158,505,590,173,506,128,156,588,171,504,126,157,592,168,508,123,161,593,169,509,124,159,591,170,507,125,160,503,587,118,163,153,501,585,119,164,154,502,586,117,162,155,583,499,121,166,152,584,500,122,167,150,582,498,120,165,151,700,699,693,697,577,294,114,282,469,578,295,470,115,283,576,296,468,116,284,580,297,472,113,285,581,298,473,111,286,579,299,471,112,287,467,575,105,300,288,465,573,106,301,289,466,574,107,302,290,571,463,108,303,291,572,464,109,304,292,570,462,110,305,293,681,679,676,675,517,202,179,191,601,518,203,602,177,189,516,201,600,178,190,520,198,604,175,187,521,199,605,176,188,519,200,603,174,186,599,515,185,208,197,597,513,183,209,195,598,514,184,207,196,511,595,181,204,193,512,596,182,205,194,510,594,180,206,192,684,678,682,680,27,529,76,101,278,28,530,276,77,99,29,528,277,75,100,26,532,281,79,104,24,533,279,80,102,25,531,280,78,103,273,33,74,527,96,274,34,72,525,97,275,35,73,526,98,32,272,70,523,95,30,270,71,524,93,31,271,69,522,94,689,685,691,690 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#e2a478bba1a9cde7c476f091d01301457f542f6a1b857d9784efc8df77c998e9, 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 21:17:02 · history