Equation 677 Database

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Magma 165393264ea9…

magma 165393264ea9
Size
705
Isomorphism class hash
165393264ea9df18571120da4a47e7e191b6e93182460e0c04be0d981d05b2b1
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 19:08:42
Display reorder
660,610,613,608,615,122,630,120,633,628,635,653,121,650,648,655,125,590,593,588,595,123,550,553,548,555,124,570,573,568,575,128,431,429,427,433,126,453,450,448,455,127,473,470,468,475,493,131,490,488,495,508,513,129,510,515,533,130,530,528,535,685,691,697,688,606,617,614,611,234,626,235,637,634,631,657,236,646,654,651,237,586,597,594,591,238,546,557,554,551,239,566,577,574,571,232,435,425,432,430,233,457,446,454,451,231,477,466,474,471,497,228,486,494,491,514,517,229,506,511,537,230,526,534,531,698,694,703,686,417,345,321,369,82,418,83,346,322,370,347,81,419,323,371,78,416,344,320,368,79,414,342,318,366,80,415,343,319,367,73,336,408,312,360,74,337,409,313,361,72,338,410,314,362,339,76,411,315,363,316,340,77,412,364,341,75,413,317,365,664,671,669,681,393,33,105,405,183,394,184,34,106,406,35,185,395,107,407,182,392,32,104,404,180,390,30,102,402,181,391,31,103,403,189,24,384,96,396,190,25,385,97,397,191,26,386,98,398,27,188,387,99,399,100,28,186,388,400,29,187,389,101,401,673,678,667,675,607,619,616,609,221,627,219,639,636,629,659,220,647,656,649,217,587,599,596,589,218,547,559,556,549,216,567,579,576,569,227,439,426,434,428,225,459,447,456,449,226,479,467,476,469,499,223,487,496,489,516,519,224,507,509,539,222,527,536,529,701,687,690,689,612,601,603,602,135,632,136,620,623,622,640,137,652,643,642,134,592,581,583,582,132,552,541,543,542,133,572,561,563,562,141,438,422,421,420,142,441,452,443,442,143,461,472,463,462,480,140,492,482,481,502,500,138,512,501,521,139,532,522,520,696,695,699,693,600,604,618,605,9,621,10,624,638,625,644,11,641,658,645,8,580,584,598,585,6,540,544,558,545,7,560,564,578,565,1,437,424,436,423,0,444,440,458,445,2,464,460,478,465,483,3,485,498,484,518,503,4,505,504,523,5,525,538,524,704,702,700,692,282,297,273,260,200,283,198,298,274,258,299,199,284,275,259,203,285,296,272,263,201,286,294,270,261,202,287,295,271,262,195,288,280,264,255,196,289,281,265,256,197,290,279,266,257,291,194,276,267,254,268,292,192,277,252,293,193,278,269,253,662,676,663,679,381,151,178,161,93,382,94,152,179,159,150,95,383,177,160,92,380,154,174,157,90,378,155,175,158,91,379,153,176,156,84,149,372,169,167,85,147,373,170,165,86,148,374,168,166,145,87,375,172,163,173,146,88,376,164,144,89,377,171,162,661,683,665,674,51,115,46,357,300,52,301,116,47,358,114,302,53,45,359,303,50,118,42,356,304,48,119,43,354,305,49,117,44,355,306,113,57,37,348,307,111,58,38,349,308,112,59,36,350,109,309,56,40,351,41,110,310,54,352,108,311,55,39,353,668,670,684,682,212,248,333,21,69,210,70,246,334,22,247,71,211,335,23,68,215,251,332,20,66,213,249,330,18,67,214,250,331,19,60,243,207,324,12,61,244,208,325,13,62,245,209,326,14,242,63,206,327,15,328,240,64,204,16,241,65,205,329,17,666,677,672,680 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#8819209ab5a908e1474d8d2e3196687ec1a856ed03900dcfe11c102e06a1cf49, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 19:08:43 · history