Equation 677 Database

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Magma a283bcc79d91…

magma a283bcc79d91
Size
705
Isomorphism class hash
a283bcc79d91e8ef5426fe2d3be0b3310539c036be62caa90c877283b0fc3a12
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 15:17:37
Display reorder
660,299,356,278,269,262,354,297,276,267,263,277,355,268,261,298,281,295,359,265,258,296,279,357,266,259,294,280,358,264,260,284,351,290,275,253,282,352,288,273,254,283,353,289,274,252,271,350,287,293,256,348,285,291,272,257,349,286,292,270,255,668,662,661,672,124,83,404,175,614,81,125,402,176,612,403,82,174,613,123,407,120,79,178,617,121,405,80,179,615,122,406,78,177,616,399,89,130,173,609,400,87,131,171,610,401,88,129,172,611,169,85,398,126,608,86,396,127,170,606,84,397,128,168,607,690,689,685,686,323,584,452,512,392,582,321,450,510,390,451,583,511,391,322,455,319,587,515,395,320,453,585,513,393,318,454,586,514,394,447,579,314,507,387,448,580,312,508,388,449,581,313,509,389,506,578,446,317,386,576,444,315,504,384,577,445,316,505,385,669,663,670,666,185,476,602,500,532,474,183,600,498,529,601,475,499,530,184,605,181,479,503,538,182,603,477,501,535,180,604,478,502,536,597,471,191,495,523,598,472,189,496,525,599,473,190,497,526,494,470,596,187,520,468,594,188,492,516,469,595,186,493,518,676,678,675,682,192,428,440,18,133,426,193,438,19,134,439,427,20,132,194,443,195,431,21,136,196,441,429,22,137,197,442,430,23,135,435,423,198,24,139,436,424,199,25,140,437,425,200,26,138,27,422,434,201,142,420,432,202,28,143,421,433,203,29,141,671,667,664,665,67,300,560,572,8,301,68,558,570,6,559,302,571,7,66,563,70,303,575,11,71,561,304,573,9,69,562,305,574,10,555,306,73,567,14,556,307,74,568,12,557,308,72,569,13,566,309,554,76,17,310,552,77,564,15,311,553,75,565,16,697,694,693,696,98,644,647,646,645,638,96,639,637,636,643,640,642,641,97,659,101,656,658,657,99,651,649,650,648,100,655,653,654,652,621,589,104,93,5,622,590,102,94,3,623,588,103,95,4,92,592,620,107,0,593,618,105,90,2,591,619,106,91,1,703,701,702,704,151,629,217,628,488,624,152,218,625,486,216,626,627,487,150,220,154,634,635,491,155,221,631,630,489,153,219,633,632,490,223,205,149,213,483,224,206,147,214,484,222,204,148,215,485,212,208,226,145,482,209,227,146,210,480,207,225,144,211,481,700,695,699,698,41,343,374,464,416,344,39,372,462,414,373,342,463,415,40,377,37,346,467,419,38,375,347,465,417,36,376,345,466,418,380,341,32,459,411,378,339,30,460,412,379,340,31,461,413,458,337,383,35,410,338,381,33,456,408,336,382,34,457,409,674,684,679,680,167,245,235,118,533,243,165,236,119,528,234,244,117,531,166,238,163,241,114,539,164,239,242,115,534,162,237,240,116,537,233,251,158,109,522,231,249,156,110,524,232,250,157,108,527,112,247,229,161,521,248,230,159,113,517,246,228,160,111,519,683,677,681,673,368,51,54,548,331,52,366,55,546,332,56,53,547,330,367,57,371,50,551,334,369,58,48,549,335,370,59,49,550,333,60,42,363,543,329,61,43,364,544,327,62,44,365,545,328,542,45,63,362,325,46,64,360,540,326,47,65,361,541,324,687,691,688,692 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#101de34e785e3f92e4e627a1da3ddc1fe7ebde0c6c88cd6039e0733ba8ec0ae0, 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 15:17:38 · history