Equation 677 Database

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Magma 1d0235553e39…

magma 1d0235553e39
Size
705
Isomorphism class hash
1d0235553e3974f0a683573dd95f98dc87ad59d2d50fbba318b8a122c3a209d5
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 21:10:49
Display reorder
704,445,441,460,487,446,461,488,442,444,443,459,486,456,448,440,490,457,449,438,491,458,447,439,489,466,451,485,432,467,452,483,433,465,450,484,434,454,462,481,435,455,463,482,436,453,464,480,437,472,473,471,468,469,470,478,479,476,474,475,477,702,701,703,700,656,659,657,658,649,648,650,651,652,655,653,654,641,640,643,642,645,644,647,646,636,637,639,638,620,621,622,623,612,613,614,615,616,617,618,619,632,633,634,635,625,624,626,627,629,628,630,631,0,2,1,4,5,3,7,8,9,10,11,6,690,689,691,688,253,83,268,291,254,269,292,81,252,82,267,293,264,256,79,290,265,257,80,288,266,255,78,289,274,259,297,74,275,260,298,72,273,258,299,73,262,270,296,77,263,271,294,75,261,272,295,76,279,280,281,278,276,277,285,286,283,284,282,287,673,674,672,675,383,318,341,363,381,339,364,319,382,320,340,365,337,379,321,362,338,380,322,360,336,378,323,361,347,374,369,316,345,372,370,317,346,373,371,315,377,343,368,312,375,344,366,313,376,342,367,314,348,349,350,351,352,353,354,355,359,357,358,356,680,683,681,682,177,193,139,159,178,140,160,194,179,192,138,161,142,176,196,158,143,174,197,156,141,175,195,157,137,168,165,199,135,169,166,200,136,170,167,198,171,133,164,202,172,134,162,203,173,132,163,201,144,145,146,147,148,149,150,151,155,153,154,152,694,692,693,695,414,324,422,398,415,420,396,325,416,326,421,397,425,417,327,401,423,418,328,399,424,419,329,400,428,412,404,330,426,413,402,331,427,411,403,332,408,431,407,333,409,429,405,334,410,430,406,335,395,393,394,391,392,390,386,384,388,389,387,385,699,697,698,696,537,555,502,526,538,503,527,556,539,557,501,525,498,536,554,522,499,534,552,523,500,535,553,524,493,528,517,561,494,529,518,562,492,530,516,563,531,496,520,560,532,497,521,558,533,495,519,559,512,510,511,515,513,514,507,508,505,506,504,509,687,685,684,686,92,188,104,128,90,102,126,186,91,187,103,127,107,95,191,131,105,93,189,129,106,94,190,130,99,87,123,183,100,88,124,184,101,89,125,185,86,98,122,182,84,96,120,180,85,97,121,181,118,119,117,114,115,116,109,110,111,112,113,108,660,663,661,662,210,300,216,250,211,217,251,301,212,302,218,249,219,213,303,246,220,214,304,247,221,215,305,248,222,208,241,306,223,209,242,307,224,207,240,308,204,225,244,309,205,226,245,310,206,227,243,311,236,234,235,239,237,238,231,232,229,230,228,233,677,678,676,679,54,17,61,47,55,62,45,15,56,16,60,46,64,57,13,43,65,58,14,44,63,59,12,42,67,52,38,23,68,53,36,21,66,51,37,22,48,70,41,19,49,71,39,20,50,69,40,18,25,26,24,28,29,27,31,32,33,34,35,30,664,667,665,666,573,551,578,603,574,576,604,549,575,550,577,605,581,572,547,602,579,570,548,600,580,571,546,601,584,564,609,542,582,565,610,540,583,566,611,541,567,587,608,545,568,585,606,543,569,586,607,544,597,598,599,596,594,595,588,589,593,591,592,590,669,671,670,668 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#dc3952d3945a57ff89efbf9c91902a27e7bb606727f60175866197715516bbc5, 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 21:10:49 · history