Equation 677 Database

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Magma d7cb213cb713…

magma d7cb213cb713
Size
705
Isomorphism class hash
d7cb213cb713f5ec392d9702773f5a3efb591626803f3aacd1f3b163a3eeee1c
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 21:20:47
Display reorder
660,167,647,646,650,651,165,611,607,606,610,166,631,627,626,630,567,163,571,566,570,587,164,591,586,590,547,162,551,546,550,158,467,471,466,470,431,427,426,156,430,451,447,446,157,450,527,531,526,161,530,487,491,486,159,490,507,511,506,160,510,685,694,690,689,11,648,641,649,658,9,618,608,600,609,10,638,628,620,629,568,7,578,561,569,588,8,598,581,589,548,6,558,540,549,2,468,478,461,469,436,428,421,1,429,458,448,440,0,449,528,538,520,5,529,488,498,481,3,489,508,518,501,4,509,693,701,697,703,32,371,226,214,237,30,238,369,227,215,31,239,370,225,213,367,35,236,222,210,368,33,234,223,211,366,34,235,224,212,27,362,228,217,205,229,360,218,28,206,230,361,216,29,204,365,231,220,26,208,363,232,221,24,209,364,233,219,25,207,662,680,671,665,91,140,115,407,42,92,43,138,116,405,90,44,139,114,406,143,94,45,118,403,141,95,46,119,404,142,93,47,117,402,89,135,40,113,398,41,136,111,87,396,39,137,112,88,397,134,36,109,85,401,132,37,110,86,399,133,38,108,84,400,669,676,678,664,201,653,642,652,640,202,601,613,602,612,203,621,633,622,632,573,200,560,562,572,593,198,580,582,592,553,199,541,542,552,192,473,460,462,472,422,439,437,193,438,441,453,442,194,452,533,521,522,195,532,493,480,482,196,492,513,500,502,197,512,695,688,686,699,53,657,643,655,659,51,619,617,603,615,52,639,637,623,635,577,49,579,563,575,597,50,599,583,595,557,48,559,543,555,59,477,479,463,475,420,435,423,57,433,459,457,443,58,455,537,539,523,55,535,497,499,483,56,495,517,519,503,54,515,704,698,702,691,171,656,645,654,644,172,604,616,605,614,173,624,636,625,634,576,170,564,565,574,596,168,584,585,594,556,169,544,545,554,177,476,464,465,474,424,434,425,178,432,444,456,445,179,454,536,524,525,176,534,496,484,485,174,494,516,504,505,175,514,687,696,700,692,16,251,265,419,287,17,285,249,266,417,15,286,250,264,418,247,12,283,268,415,248,13,284,269,416,246,14,282,267,414,22,242,278,271,410,276,240,272,23,408,277,241,270,21,409,245,281,274,18,413,243,279,275,19,411,244,280,273,20,412,681,684,675,661,79,301,347,325,98,80,96,302,345,326,78,97,300,346,324,304,82,101,343,328,305,83,99,344,329,303,81,100,342,327,77,307,104,338,331,102,308,336,75,332,103,306,337,76,330,310,107,341,73,334,311,105,339,74,335,309,106,340,72,333,668,667,683,674,150,125,395,383,299,151,297,123,393,381,152,298,124,394,382,121,153,295,391,379,122,154,296,392,380,120,155,294,390,378,148,131,290,386,374,288,129,384,149,372,289,130,385,147,373,127,293,389,144,377,128,291,387,145,375,126,292,388,146,376,673,672,663,666,71,181,317,359,254,69,252,182,315,357,70,253,180,316,358,184,67,257,313,355,185,68,255,314,356,183,66,256,312,354,62,187,260,323,350,258,188,321,60,348,259,186,322,61,349,190,263,319,65,353,191,261,320,63,351,189,262,318,64,352,677,670,679,682 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#ea8bb88472b4cb0aad957f1394df72437c069594286fecb60b6451f1d57bec9b, 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 21:20:48 · history