Equation 677 Database

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Magma 32378c324614…

magma 32378c324614
Size
705
Isomorphism class hash
32378c3246148db74f04459fd90d4e5fd67f1a432f4b4309d563e9978675f162
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 19:52:19
Display reorder
660,238,505,541,459,116,239,117,506,542,460,240,115,507,543,461,119,237,504,540,458,120,235,502,538,456,118,236,503,539,457,496,229,114,532,450,497,230,112,533,451,534,498,231,113,452,232,499,110,535,453,233,500,111,536,454,234,501,109,537,455,669,665,667,666,316,529,304,471,49,317,50,530,305,472,315,48,531,303,473,45,312,528,300,470,46,313,526,301,468,47,314,527,302,469,520,307,40,295,462,521,308,41,296,463,294,522,306,39,464,310,523,43,298,465,311,524,44,299,466,309,525,42,297,467,690,687,688,685,517,411,577,635,255,518,253,412,578,636,519,254,413,579,637,258,516,410,576,634,256,514,408,574,632,257,515,409,575,633,402,508,261,568,626,403,509,259,569,627,570,404,510,260,628,511,405,264,571,629,512,406,262,572,630,513,407,263,573,631,670,672,664,668,399,329,162,447,283,400,284,327,160,448,401,282,328,161,449,286,398,325,158,446,287,396,326,159,444,285,397,324,157,445,320,390,289,168,438,318,391,290,166,439,167,319,392,288,440,393,323,292,164,441,394,321,293,165,442,395,322,291,163,443,682,677,680,675,351,387,332,611,133,352,134,388,330,612,353,135,389,331,613,136,350,386,335,610,137,348,384,333,608,138,349,385,334,609,378,342,139,338,602,379,343,140,336,603,337,380,344,141,604,345,381,142,341,605,346,382,143,339,606,347,383,144,340,607,662,671,663,661,553,435,375,55,241,554,242,436,376,56,555,243,437,377,54,244,552,434,374,51,245,550,432,372,52,246,551,433,373,53,426,544,247,366,61,427,545,248,367,62,368,428,546,249,60,547,429,250,369,57,548,430,251,370,58,549,431,252,371,59,694,693,695,696,647,480,275,274,146,655,147,654,653,652,659,145,658,657,656,149,646,481,2,273,150,644,482,1,271,148,645,483,0,272,478,638,152,281,265,479,639,153,279,266,280,477,640,151,267,641,474,155,277,268,642,475,156,278,269,643,476,154,276,270,703,702,701,704,77,598,63,128,22,78,23,648,649,129,76,21,650,651,127,25,73,599,64,131,26,74,600,65,132,24,75,601,66,130,596,83,20,71,126,597,84,18,72,124,70,595,82,19,125,79,592,16,67,122,80,593,17,68,123,81,594,15,69,121,699,697,700,698,423,106,589,623,222,424,220,107,590,624,425,221,108,591,625,218,422,105,588,622,219,420,103,586,620,217,421,104,587,621,97,414,228,580,614,98,415,226,581,615,582,99,416,227,616,417,100,224,583,617,418,101,225,584,618,419,102,223,585,619,681,684,673,676,35,363,565,493,14,33,12,364,566,494,34,13,365,567,495,10,38,362,564,492,11,36,360,562,490,9,37,361,563,491,354,30,5,556,484,355,31,3,557,485,558,356,32,4,486,29,357,8,559,487,27,358,6,560,488,28,359,7,561,489,679,678,674,683,181,195,169,214,94,182,95,193,170,215,183,96,194,171,216,93,184,198,172,213,91,185,196,173,211,92,186,197,174,212,201,187,85,175,205,199,188,86,176,206,177,200,189,87,207,190,204,88,178,208,191,202,89,179,209,192,203,90,180,210,686,692,689,691 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#b25ea76719ef85ac96ca5a21eaa9f8d56a10b2e0f8b67970c90091297d765387, 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 19:52:20 · history