Equation 677 Database

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Magma 3e3b2bea6167…

magma 3e3b2bea6167
Size
705
Isomorphism class hash
3e3b2bea6167c75be715eb4815de7ce5de7c409b4f162e78917665366fbc89a4
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 15:56:51
Display reorder
660,485,491,67,496,480,505,511,516,68,501,525,531,66,536,521,471,465,70,476,462,431,430,71,433,429,451,445,69,456,442,611,616,605,65,600,631,636,625,63,621,651,656,645,64,641,598,591,585,61,580,558,551,545,62,540,578,571,565,60,560,692,688,685,703,486,489,170,492,487,506,509,512,168,507,526,529,169,532,527,469,466,173,472,467,438,436,171,439,424,449,446,172,452,447,609,612,606,176,607,629,632,626,174,627,649,652,646,175,647,592,589,586,179,587,552,549,546,177,547,572,569,566,178,567,693,690,687,696,315,248,57,363,387,316,246,364,58,388,317,247,59,365,389,251,314,56,362,386,249,312,54,360,384,250,313,55,361,385,243,369,321,48,393,244,370,322,49,394,245,371,323,50,395,368,242,320,51,392,366,240,318,52,390,367,241,319,53,391,667,678,664,673,148,411,275,132,4,149,412,133,273,5,147,413,274,134,3,410,144,271,135,1,408,145,272,136,0,409,146,270,137,2,417,138,154,266,10,418,139,155,264,11,419,140,153,265,9,141,416,150,269,6,142,414,151,267,7,143,415,152,268,8,683,677,679,681,481,495,42,490,494,500,515,510,43,514,520,535,44,530,534,475,460,45,470,474,427,423,46,425,426,455,440,47,450,454,615,610,601,40,614,635,630,620,41,634,655,650,640,39,654,590,597,581,36,594,550,557,541,37,554,570,577,561,38,574,701,697,704,694,498,499,16,497,482,518,519,517,17,502,537,539,15,538,522,479,477,12,478,461,422,421,13,420,428,459,457,14,458,441,619,617,618,22,602,637,639,638,23,622,659,658,657,21,642,596,599,595,18,582,556,559,555,19,542,576,579,575,20,562,698,702,689,700,483,488,28,484,493,503,508,504,29,513,523,528,27,524,533,468,463,24,464,473,437,434,25,435,432,448,443,26,444,453,608,604,603,34,613,628,624,623,35,633,648,644,643,33,653,584,588,583,30,593,544,548,543,31,553,564,568,563,32,573,691,686,695,699,163,188,100,192,291,164,186,193,101,292,162,187,99,194,293,191,166,96,195,290,189,167,97,196,288,190,165,98,197,289,183,198,161,106,297,184,199,159,107,298,185,200,160,105,299,201,182,157,102,296,202,180,158,103,294,203,181,156,104,295,675,661,684,668,327,303,259,399,129,328,304,400,260,130,329,305,258,401,131,302,326,262,398,128,300,324,263,396,126,301,325,261,397,127,309,405,333,257,120,310,406,334,255,121,311,407,335,256,122,404,308,332,253,123,402,306,330,254,124,403,307,331,252,125,663,662,669,682,351,237,75,375,225,352,238,376,76,226,353,239,77,377,227,236,350,74,374,224,234,348,72,372,222,235,349,73,373,223,228,381,357,81,216,229,382,358,82,217,230,383,359,83,218,380,231,356,80,219,378,232,354,78,220,379,233,355,79,221,672,676,671,674,339,112,209,95,287,340,113,93,207,285,341,111,208,94,286,108,338,205,91,283,109,336,206,92,284,110,337,204,90,282,118,86,345,215,278,119,84,346,213,276,117,85,347,214,277,89,114,344,211,281,87,115,342,212,279,88,116,343,210,280,680,665,670,666 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#25532901b7174194dca0f8f453aa2ae473cc5b2aa34d04b35f0c3beb206af29c, 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 15:56:52 · history