Equation 677 Database

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Magma 8ae96698445c…

magma 8ae96698445c
Size
705
Isomorphism class hash
8ae96698445c1c294f6c55cee21d47762f21be6d5514fbb7638d58bfda68d75f
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 18:20:14
Display reorder
704,515,4,469,494,513,492,5,470,514,493,3,468,497,511,1,472,495,512,0,473,496,510,2,471,500,475,10,506,498,476,11,504,499,474,9,505,478,503,6,509,479,501,7,507,477,502,8,508,490,491,489,486,487,488,481,482,483,484,485,480,700,701,703,702,656,659,657,658,648,650,651,649,652,654,655,653,642,640,643,641,646,644,647,645,638,636,639,637,622,621,623,620,614,613,615,612,618,617,619,616,632,634,635,633,625,626,627,624,628,630,631,629,115,116,114,118,119,117,113,111,108,109,110,112,691,689,690,688,294,34,255,279,295,280,35,256,296,281,33,257,278,297,30,254,276,298,31,252,277,299,32,253,285,261,25,292,286,262,26,293,287,263,24,291,260,284,28,288,258,282,29,289,259,283,27,290,264,265,266,267,268,269,270,271,275,273,274,272,675,672,674,673,441,358,455,429,442,430,359,453,443,431,357,454,428,440,354,451,426,438,355,452,427,439,356,450,420,446,349,432,421,444,350,433,422,445,348,434,449,423,352,435,447,424,353,436,448,425,351,437,411,412,413,410,408,409,417,418,415,416,414,419,681,683,680,682,165,17,179,153,166,154,15,177,167,155,16,178,152,164,13,175,150,162,14,176,151,163,12,174,144,170,23,156,145,168,21,157,146,169,22,158,173,147,19,159,171,148,20,160,172,149,18,161,135,136,137,134,132,133,141,142,139,140,138,143,693,692,694,695,390,239,399,380,391,378,237,400,392,379,238,401,383,393,235,398,381,394,236,396,382,395,234,397,375,405,230,388,376,406,228,389,377,407,229,387,404,374,233,384,402,372,231,385,403,373,232,386,362,360,361,365,363,364,368,366,370,371,369,367,698,697,699,696,521,457,531,559,519,560,458,532,520,558,456,533,562,517,460,530,563,518,461,528,561,516,459,529,557,537,463,527,555,538,464,525,556,539,462,526,536,553,466,523,534,554,467,524,535,552,465,522,541,542,540,544,545,543,547,548,549,550,551,546,686,684,687,685,192,130,208,181,193,182,131,209,194,180,129,207,184,195,126,204,185,196,127,205,183,197,128,206,187,214,121,198,188,215,122,199,186,213,120,200,210,190,124,201,211,191,125,202,212,189,123,203,221,219,220,217,218,216,227,225,222,223,224,226,661,663,660,662,303,250,318,344,304,342,251,319,305,343,249,320,347,302,246,321,345,300,247,322,346,301,248,323,339,316,241,309,340,317,242,310,341,315,240,311,312,338,244,308,313,336,245,306,314,337,243,307,332,330,331,335,333,334,327,328,325,326,324,329,676,678,677,679,59,105,62,45,57,46,106,60,58,47,107,61,44,55,104,65,42,56,102,63,43,54,103,64,36,68,96,50,37,66,97,48,38,67,98,49,71,39,99,53,69,40,100,51,70,41,101,52,75,76,77,74,72,73,81,82,79,80,78,83,665,667,664,666,568,90,586,604,569,605,91,587,567,603,92,585,600,564,93,582,601,565,94,583,602,566,95,584,610,577,88,574,611,578,89,575,609,576,87,573,580,606,84,570,581,607,85,571,579,608,86,572,597,598,599,596,594,595,588,589,593,591,592,590,670,671,669,668 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#7b4d86832894383b0b7ce3dfc16e526670032b07fced110816f25e14f2157e1a, 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 18:20:17 · history