Equation 677 Database

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Magma c02f2ed9bb31…

magma c02f2ed9bb31
Size
705
Isomorphism class hash
c02f2ed9bb31e30a2c574ddf76cbff7b3faa4c4fd4ebebc3b0f68e0323f73d7b
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 17:34:32
Display reorder
660,99,189,452,372,267,97,268,190,453,373,98,269,188,454,374,102,192,270,455,371,100,193,271,456,369,101,191,272,457,370,450,105,195,273,363,103,196,274,451,364,104,194,275,449,365,198,108,276,446,366,199,106,277,447,367,197,107,278,448,368,661,671,665,669,123,443,537,261,45,121,46,444,538,262,122,44,445,539,263,126,442,43,536,264,124,440,48,534,265,125,441,47,535,266,528,129,434,38,259,127,435,39,529,260,128,436,37,530,258,437,132,41,531,255,438,130,42,532,256,439,131,40,533,257,687,688,685,689,167,395,573,621,300,168,301,396,574,622,169,302,397,575,623,166,394,299,572,620,164,392,297,570,618,165,393,298,571,619,564,173,386,291,612,174,387,292,565,613,175,388,293,566,614,389,172,294,567,615,390,170,295,568,616,391,171,296,569,617,666,662,672,670,333,219,561,407,7,334,8,220,562,408,335,9,218,563,409,336,222,10,560,406,337,223,11,558,404,338,221,12,559,405,552,331,217,5,398,332,215,6,553,399,330,216,4,554,400,213,327,0,555,401,214,328,2,556,402,212,329,3,557,403,683,680,674,679,56,360,324,549,231,57,232,361,325,550,55,230,362,326,551,59,359,234,323,548,60,357,235,321,546,58,358,233,322,547,315,54,351,229,540,52,352,227,316,541,53,353,228,317,542,354,50,225,318,543,355,51,226,319,544,356,49,224,320,545,664,667,668,663,34,597,283,467,491,35,492,598,284,468,36,493,599,282,469,33,596,490,279,466,31,594,488,280,464,32,595,489,281,465,289,25,588,482,458,26,589,483,290,459,27,590,484,288,460,591,28,485,285,461,592,29,486,286,462,593,30,487,287,463,698,696,694,693,136,527,385,145,381,137,654,655,652,653,138,656,659,657,658,135,526,382,157,148,133,524,383,155,146,134,525,384,156,147,160,142,518,379,151,143,519,380,158,149,144,520,378,159,150,521,141,375,163,154,522,139,376,161,152,523,140,377,162,153,704,703,701,702,311,647,479,503,646,309,648,649,480,504,310,651,650,481,505,314,644,645,478,502,312,641,640,476,500,313,643,642,477,501,470,306,241,238,494,307,242,239,471,495,308,240,237,472,496,1,305,236,473,497,637,303,636,474,498,639,304,638,475,499,699,700,697,695,184,96,585,83,633,182,634,94,586,84,183,635,95,587,82,187,92,632,584,79,185,93,630,582,80,186,91,631,583,81,576,179,87,624,74,180,85,625,577,75,181,86,626,578,73,90,178,627,579,77,88,176,628,580,78,89,177,629,581,76,678,684,675,681,244,204,609,515,109,245,110,205,610,516,243,111,203,611,517,247,200,112,608,514,248,201,113,606,512,246,202,114,607,513,600,250,210,115,506,251,211,116,601,507,249,209,117,602,508,206,253,118,603,509,207,254,119,604,510,208,252,120,605,511,676,673,677,682,348,431,65,418,24,349,22,432,66,416,350,23,433,64,417,347,430,20,61,421,345,428,21,62,419,346,429,19,63,420,71,339,422,15,413,340,423,13,72,414,341,424,14,70,415,425,342,18,67,412,426,343,16,68,410,427,344,17,69,411,686,690,691,692 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#58f4898eb0f0372a4c749060353e7621900aa789e1d944064f9989e660cee0fd, 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 17:34:33 · history