Equation 677 Database

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Magma 29032c4ef508…

magma 29032c4ef508
Size
705
Isomorphism class hash
29032c4ef5082d0f126e4197925786ab902064f1d3a8dbe938a00c6a29836b6b
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 15:02:58
Display reorder
660,216,287,492,599,31,217,32,285,493,600,218,33,286,494,601,215,290,34,491,598,213,288,35,489,596,214,289,36,490,597,483,207,29,282,590,484,208,30,283,591,485,209,28,284,592,210,486,25,281,593,211,487,26,279,594,212,488,27,280,595,669,666,672,670,50,133,367,384,361,51,362,131,368,385,49,360,132,366,386,53,129,357,363,383,54,130,358,364,381,52,128,359,365,382,373,56,352,139,375,374,57,353,137,376,372,55,351,138,377,59,369,355,135,378,60,370,356,136,379,58,371,354,134,380,690,689,687,685,314,504,468,408,233,312,231,505,469,409,313,232,506,470,410,310,503,236,467,407,311,501,234,465,405,309,502,235,466,406,459,305,239,495,399,460,303,237,496,400,461,304,238,497,401,308,462,242,498,402,306,463,240,499,403,307,464,241,500,404,667,665,663,662,20,480,109,516,103,21,101,481,107,517,19,102,482,108,518,23,479,99,105,515,24,477,100,106,513,22,478,98,104,514,115,18,94,471,507,113,16,92,472,508,114,17,93,473,509,14,111,97,474,510,15,112,95,475,511,13,110,96,476,512,676,673,678,680,119,575,420,348,528,120,529,576,421,349,121,530,577,422,350,118,574,527,419,347,116,572,525,417,345,117,573,526,418,346,411,125,519,566,339,412,126,520,567,340,413,127,521,568,341,124,414,522,569,342,122,415,523,570,343,123,416,524,571,344,671,664,661,668,301,388,611,563,219,302,220,389,612,564,300,221,387,613,565,297,391,222,610,562,298,392,223,608,560,299,390,224,609,561,602,292,225,394,554,603,293,226,395,555,604,291,227,393,556,295,605,228,397,557,296,606,229,398,558,294,607,230,396,559,693,697,696,695,72,549,553,82,647,70,655,654,652,653,71,659,656,657,658,68,550,646,74,83,69,551,644,75,84,67,552,645,73,85,81,63,638,547,86,79,61,639,548,87,80,62,640,546,88,66,77,641,543,89,64,78,642,544,90,65,76,643,545,91,702,703,701,704,140,170,1,623,456,141,457,648,649,624,142,458,650,651,625,143,171,455,174,622,144,172,453,175,620,145,173,454,176,621,181,146,447,168,614,182,147,448,169,615,180,148,449,167,616,149,177,450,164,617,150,178,451,165,618,151,179,452,166,619,700,699,698,694,40,256,12,432,276,41,277,257,10,433,42,278,255,11,434,39,259,275,8,431,37,260,273,9,429,38,258,274,7,430,3,46,267,262,423,0,47,268,263,424,2,48,269,261,425,45,6,270,265,426,43,4,271,266,427,44,5,272,264,428,684,681,674,675,153,206,184,635,540,154,541,204,185,636,152,542,205,183,637,156,202,539,187,634,157,203,537,188,632,155,201,538,186,633,190,159,531,197,626,191,160,532,195,627,189,158,533,196,628,162,193,534,200,629,163,194,535,198,630,161,192,536,199,631,682,677,683,679,247,444,336,587,322,248,323,445,337,588,246,321,446,338,589,243,443,325,335,586,244,441,326,333,584,245,442,324,334,585,327,253,320,435,578,328,254,318,436,579,329,252,319,437,580,249,330,316,438,581,250,331,317,439,582,251,332,315,440,583,688,686,692,691 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#003b1571ae5bf3b67323fc5b960381c29f1c759a7de9437dd38ba69e115a500f, 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 15:03:00 · history