Equation 677 Database

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Magma 5d6e5ed7de6b…

magma 5d6e5ed7de6b
Size
705
Isomorphism class hash
5d6e5ed7de6b9ffa0fb3a9ac7fc57575a3fe62c8059db25d38c1c07a8d8b842c
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 20:40:25
Display reorder
660,597,594,62,583,599,557,554,60,543,559,577,574,61,563,579,643,654,657,65,659,63,617,614,603,619,634,637,623,639,64,494,68,497,483,499,512,66,515,502,517,67,534,537,523,539,475,71,472,461,477,69,430,435,434,436,452,70,455,441,457,696,694,699,691,593,592,261,598,596,553,552,262,558,556,573,572,263,578,576,658,652,653,260,656,258,613,612,618,616,632,633,638,636,259,492,252,493,498,496,510,253,511,516,514,254,532,533,538,536,471,255,470,476,474,256,429,437,439,438,450,257,451,456,454,695,685,688,698,356,392,217,284,174,354,390,218,282,175,355,391,216,283,176,287,395,359,220,177,221,357,393,285,178,394,358,286,179,219,387,223,351,279,172,388,224,352,280,173,222,389,353,281,171,350,226,386,278,168,227,384,348,276,169,385,225,349,277,170,661,681,668,677,121,147,73,139,368,122,148,74,140,366,120,149,72,138,367,142,146,124,76,371,77,125,144,143,369,145,123,141,370,75,153,79,127,137,363,154,80,128,135,364,78,155,126,136,365,130,82,152,133,362,83,150,131,134,360,151,81,129,132,361,666,671,680,674,587,586,289,585,584,547,546,290,545,544,567,566,288,565,564,645,646,647,292,644,293,607,606,605,604,626,627,625,624,291,486,295,487,485,484,519,296,505,504,503,294,526,527,525,524,465,298,479,464,463,299,432,427,426,425,459,297,445,444,443,693,687,701,703,580,581,56,582,595,541,540,54,542,555,560,561,55,562,575,642,640,641,59,655,57,600,601,602,615,620,621,622,635,58,480,51,481,482,495,518,52,501,500,513,53,520,521,522,535,460,50,478,462,473,48,433,424,423,431,458,49,442,440,453,702,689,692,686,588,591,10,590,589,548,551,11,550,549,568,571,9,570,569,650,651,648,6,649,7,608,611,610,609,631,628,630,629,8,491,0,488,490,489,509,2,506,508,507,1,531,528,530,529,466,4,469,468,467,5,428,420,422,421,449,3,446,448,447,704,690,700,697,268,308,235,84,248,269,306,236,85,246,267,307,234,86,247,87,311,264,238,251,239,265,309,88,249,310,266,89,250,237,303,233,274,90,243,304,231,275,91,244,232,305,273,92,245,270,229,302,93,242,230,300,271,94,240,301,228,272,95,241,675,683,670,663,116,332,23,186,404,114,330,21,187,402,115,331,22,188,403,189,335,119,19,407,20,117,333,190,405,334,118,191,406,18,327,14,111,184,399,328,12,112,185,400,13,329,113,183,401,110,17,326,180,398,15,324,108,181,396,325,16,109,182,397,676,679,672,665,380,46,29,166,212,378,47,27,167,210,379,45,28,165,211,162,42,383,25,215,26,381,43,163,213,44,382,164,214,24,37,35,375,157,207,38,33,376,158,208,34,36,377,156,209,374,31,40,160,206,32,41,372,161,204,39,30,373,159,205,678,669,673,682,195,320,96,344,416,196,318,97,342,414,197,319,98,343,415,347,323,194,99,419,100,192,321,345,417,322,193,346,418,101,315,102,201,339,411,316,103,202,340,412,104,317,203,341,413,200,105,314,338,410,106,312,198,336,408,313,107,199,337,409,667,684,662,664 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#cb0e3d6c08ee89c5c6b2b247efbea2db23079510829d72f3f07184542ed1a6a6, 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 20:40:26 · history