Equation 677 Database

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Magma 2c56c9601506…

magma 2c56c9601506
Size
705
Isomorphism class hash
2c56c96015061cb243dc53cdaad180409b7825ba60828d46897d2a24e4706d3b
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 21:56:12
Display reorder
660,543,145,387,495,459,496,146,544,388,460,542,144,386,494,458,148,546,390,498,462,149,547,391,499,463,147,545,389,497,461,541,385,151,493,457,539,383,152,491,455,540,384,150,492,456,381,537,154,489,453,382,538,155,490,454,380,536,153,488,452,669,668,671,664,333,126,447,483,44,484,127,334,448,45,332,128,446,482,46,129,336,450,486,47,130,337,451,487,48,131,335,449,485,49,339,445,124,481,42,340,443,125,479,43,338,444,123,480,41,441,342,120,477,38,442,343,121,478,39,440,341,122,476,40,688,685,687,686,555,75,166,303,399,304,76,556,167,400,554,77,165,302,398,74,558,162,306,402,72,559,163,307,403,73,557,164,305,401,553,157,81,301,397,551,158,82,299,395,552,156,83,300,396,160,549,80,297,393,161,550,78,298,394,159,548,79,296,392,663,665,672,662,268,308,351,363,274,364,309,266,352,272,267,310,350,362,273,311,271,354,366,277,312,269,355,367,275,313,270,353,365,276,263,349,314,361,280,264,347,315,359,278,265,348,316,360,279,345,262,317,357,283,346,260,318,358,281,344,261,319,356,282,675,673,680,674,291,331,411,423,228,424,329,292,412,229,290,330,410,422,227,327,294,414,426,224,328,295,415,427,225,326,293,413,425,226,289,409,322,421,234,287,407,320,419,235,288,408,321,420,233,405,285,325,417,230,406,286,323,418,231,404,284,324,416,232,667,670,661,666,531,255,6,181,179,182,256,532,7,177,530,254,5,180,178,258,534,2,184,175,259,535,3,185,176,257,533,4,183,174,529,12,253,187,170,527,13,251,188,168,528,11,252,186,169,8,525,249,190,173,9,526,250,191,171,10,524,248,189,172,696,698,695,693,611,212,567,65,211,646,213,647,644,645,610,214,566,64,210,215,655,652,653,654,216,659,656,657,658,217,651,649,648,650,609,561,218,68,209,607,562,219,66,207,608,560,220,67,208,564,605,221,71,205,565,606,222,69,206,563,604,223,70,204,703,701,704,702,634,15,587,635,507,637,16,636,588,508,633,14,586,632,506,18,640,590,641,510,19,642,591,643,511,17,639,589,638,509,630,585,21,631,505,627,583,22,626,503,628,584,20,629,504,581,50,24,0,501,582,625,25,624,502,580,51,23,1,500,700,694,699,697,143,110,435,619,575,620,108,141,436,576,142,109,434,618,574,113,139,438,622,578,111,140,439,623,579,112,138,437,621,577,134,433,116,617,573,132,431,114,615,571,133,432,115,616,572,429,137,119,613,569,430,135,117,614,570,428,136,118,612,568,684,682,679,677,28,58,599,375,471,376,59,26,600,472,27,60,598,374,470,61,31,602,378,474,62,29,603,379,475,63,30,601,377,473,34,597,56,373,469,32,595,57,371,467,33,596,55,372,468,593,37,52,369,465,594,35,53,370,466,592,36,54,368,464,676,678,681,683,199,241,106,519,86,520,239,200,107,84,198,240,105,518,85,237,202,102,522,89,238,203,103,523,87,236,201,104,521,88,197,97,247,517,92,195,98,245,515,90,196,96,246,516,91,100,193,243,513,95,101,194,244,514,93,99,192,242,512,94,689,691,690,692 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#fd865ad85ec1badfd7a7711949755519f1db0e961ea1bdb330ad04fd991385b2, 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 21:56:13 · history