Equation 677 Database

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Magma e6e04edffb0b…

magma e6e04edffb0b
Size
705
Isomorphism class hash
e6e04edffb0bc48f64c339f77fceeb75c60c994acbcb81ca211ef075140bba19
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 19:52:43
Display reorder
660,70,493,482,488,490,71,508,513,502,510,533,528,69,522,530,66,473,463,468,470,432,67,428,430,431,68,453,442,448,450,61,613,603,608,610,62,633,623,628,630,653,60,643,648,650,593,64,583,588,590,553,65,543,548,550,573,63,563,568,570,691,688,686,698,28,495,487,492,489,29,512,515,507,509,535,532,27,527,529,24,475,467,472,469,438,25,436,437,426,26,455,447,452,449,34,615,607,612,609,35,635,627,632,629,655,33,647,652,649,595,30,587,592,589,555,31,547,552,549,575,32,567,572,569,689,690,687,699,59,279,411,363,242,57,364,280,412,240,281,365,58,413,241,55,278,410,362,245,276,56,408,360,243,54,277,409,361,244,50,285,417,369,248,48,286,418,370,246,287,49,419,371,247,284,53,416,368,251,282,51,414,366,249,283,52,415,367,250,662,675,681,663,169,303,339,289,154,170,290,304,340,155,305,288,168,341,153,172,302,338,292,150,300,173,336,293,151,171,301,337,291,152,175,309,345,295,145,176,310,346,296,146,311,174,347,294,144,308,178,344,298,148,306,179,342,299,149,307,177,343,297,147,672,670,669,665,120,485,484,486,491,121,506,505,504,511,525,526,122,524,531,123,465,464,466,471,424,124,423,425,427,125,445,444,446,451,126,605,604,606,611,127,625,624,626,631,645,128,644,646,651,585,129,584,586,591,545,130,544,546,551,565,131,564,566,571,692,702,696,703,93,498,497,499,483,94,519,518,517,503,537,539,95,538,523,92,477,478,479,460,421,90,420,422,429,91,457,458,459,443,84,617,618,619,600,85,638,637,639,621,658,86,657,659,641,597,87,598,599,580,558,88,557,559,540,577,89,578,579,560,697,685,693,694,82,496,480,481,494,83,501,516,500,514,536,521,81,520,534,78,476,462,461,474,439,79,435,434,433,80,456,440,441,454,73,616,602,601,614,74,636,622,620,634,656,72,642,640,654,596,76,582,581,594,556,77,542,541,554,576,75,562,561,574,701,704,695,700,142,190,203,327,213,143,328,191,201,214,189,329,141,202,215,138,186,199,326,212,187,139,200,324,210,140,188,198,325,211,133,181,194,333,204,134,182,192,334,205,180,132,193,335,206,184,136,197,332,207,185,137,195,330,208,183,135,196,331,209,671,668,678,682,159,351,3,96,399,160,97,352,4,400,353,98,161,5,401,158,350,2,99,398,348,156,1,100,396,157,349,0,101,397,165,357,9,102,405,166,358,10,103,406,359,167,11,104,407,356,164,8,105,404,354,162,6,106,402,355,163,7,107,403,679,683,684,673,45,315,387,275,259,46,273,316,388,260,317,274,47,389,258,44,314,386,271,262,312,42,384,272,263,43,313,385,270,261,36,321,393,266,257,37,322,394,264,255,323,38,395,265,256,320,39,392,269,253,318,40,390,267,254,319,41,391,268,252,674,680,677,667,224,228,12,375,116,222,376,229,13,114,230,377,223,14,115,227,231,15,374,119,232,225,16,372,117,226,233,17,373,118,219,234,18,381,111,220,235,19,382,112,236,221,20,383,113,237,218,21,380,110,238,216,22,378,108,239,217,23,379,109,661,676,664,666 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#b2f3cd20f8767e98b3e6e1e1383f90e37f2ce11df778eec5ffdbe92cabb78104, 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 19:52:44 · history