Equation 677 Database

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Magma b608531cd42c…

magma b608531cd42c
Size
705
Isomorphism class hash
b608531cd42c0f3b87bcb45bafd1e1fb329a908cc291adaba34eee3253ce3686
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 19:07:06
Display reorder
704,482,459,471,513,472,483,514,460,470,458,484,512,455,467,481,509,456,468,479,510,457,469,480,511,477,465,504,488,478,466,505,489,476,464,503,490,461,473,507,487,462,474,508,485,463,475,506,486,501,502,500,497,498,499,492,493,494,495,496,491,700,702,701,703,656,658,657,659,649,648,651,650,653,654,652,655,642,641,640,643,646,645,644,647,638,637,636,639,620,622,623,621,612,614,615,613,616,618,619,617,634,632,635,633,626,625,627,624,630,628,631,629,30,31,32,33,34,611,28,29,26,24,25,27,688,691,690,689,239,21,283,264,281,240,265,22,282,23,241,263,20,286,242,267,18,284,243,268,19,285,244,266,278,12,270,245,279,13,271,246,280,14,269,247,15,277,273,248,16,275,274,249,17,276,272,250,252,253,251,255,256,254,258,259,260,261,262,257,675,672,673,674,405,340,442,422,440,406,423,338,441,339,404,424,336,438,401,421,337,439,402,419,335,437,403,420,433,346,428,396,431,344,429,397,432,345,430,395,342,436,427,399,343,434,425,400,341,435,426,398,407,408,409,410,411,412,413,414,418,416,417,415,682,681,680,683,101,46,131,126,132,102,127,44,133,45,103,125,42,134,104,129,43,135,105,130,41,136,106,128,137,37,124,99,138,35,122,100,139,36,123,98,40,140,120,95,38,141,121,96,39,142,119,97,114,115,113,117,118,116,112,110,107,108,109,111,695,693,694,692,351,3,388,375,386,352,376,4,387,5,350,374,2,384,347,371,1,385,348,372,0,383,349,373,394,9,381,357,392,10,382,358,393,11,380,356,8,390,377,353,6,391,378,354,7,389,379,355,364,362,363,360,361,359,370,368,365,366,367,369,696,698,699,697,543,445,538,518,536,544,519,443,537,444,542,520,448,534,539,517,446,535,540,515,447,533,541,516,529,451,524,549,527,449,525,550,528,450,526,548,454,532,523,545,452,530,521,546,453,531,522,547,555,556,554,551,552,553,561,562,559,557,558,560,686,687,684,685,47,154,93,79,94,48,77,152,92,153,49,78,150,89,50,82,151,90,51,80,149,91,52,81,84,145,74,53,85,143,75,54,83,144,76,55,148,87,73,56,146,88,71,57,147,86,72,58,61,59,60,64,62,63,67,65,69,70,68,66,662,661,660,663,323,235,318,305,319,324,306,233,317,234,325,307,238,321,326,308,236,322,327,309,237,320,328,310,316,230,303,329,314,231,304,330,315,232,302,331,229,312,299,332,227,313,300,333,228,311,301,334,294,295,293,297,298,296,292,290,287,288,289,291,679,676,677,678,164,211,201,182,202,165,183,209,200,210,166,184,214,197,163,181,212,198,161,179,213,199,162,180,192,206,188,155,193,207,189,156,191,208,190,157,205,195,187,158,203,196,185,159,204,194,186,160,176,177,178,175,173,174,167,168,172,170,171,169,667,664,665,666,574,226,610,595,608,572,593,224,609,225,573,594,222,606,570,598,223,607,571,596,221,605,569,597,601,217,590,565,599,215,591,563,600,216,592,564,220,604,589,568,218,602,587,566,219,603,588,567,578,579,580,577,575,576,584,585,582,583,581,586,668,670,669,671 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#8782a898cb34e59b9ea1a81d727d55f661339e265a029f2d4530f64cefd9daa9, 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 19:07:07 · history