Equation 677 Database

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Magma 64915e28c9ee…

magma 64915e28c9ee
Size
705
Isomorphism class hash
64915e28c9ee97368dfb24f93d596afa78751b00aec760dbb67d392a051f8027
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 21:57:24
Display reorder
660,80,518,512,508,509,78,538,532,528,529,79,498,492,488,489,438,83,432,428,429,451,450,448,449,81,478,82,472,468,469,75,632,638,628,629,76,652,658,648,649,77,612,618,608,609,552,74,558,548,549,568,572,72,578,569,592,73,598,588,589,698,688,690,697,109,510,503,517,519,110,530,523,537,539,108,490,483,497,499,430,112,424,437,439,457,452,458,459,113,470,111,464,477,479,115,624,630,637,639,116,644,650,657,659,114,604,610,617,619,544,118,550,557,559,577,564,119,570,579,584,117,590,597,599,685,699,696,687,296,107,352,196,316,294,105,353,197,317,295,106,351,195,315,103,299,348,192,312,104,349,193,313,297,102,298,350,194,314,291,358,98,202,322,292,359,96,203,323,293,357,97,201,321,354,290,101,198,318,199,355,288,99,319,356,289,100,200,320,662,664,668,680,237,158,173,149,364,238,156,171,147,365,239,157,172,148,363,161,236,169,145,360,159,170,146,361,234,160,235,168,144,362,228,179,164,155,370,229,177,162,153,371,230,178,163,154,369,175,231,167,151,366,152,176,232,165,367,174,233,166,150,368,674,669,665,675,209,516,514,511,502,207,536,534,531,522,208,496,494,491,482,436,205,434,431,423,447,446,445,444,206,476,204,474,471,463,215,634,636,631,623,213,654,656,651,643,214,614,616,611,603,554,211,556,551,543,571,574,212,576,563,594,210,596,591,583,689,686,692,694,62,515,513,500,501,60,535,533,521,520,61,495,493,480,481,435,65,433,421,422,443,442,440,441,63,475,64,473,460,462,68,633,635,621,622,66,653,655,640,642,67,613,615,601,602,553,71,555,541,542,561,573,69,575,562,593,70,595,580,582,695,700,691,693,55,505,506,504,507,56,525,526,524,527,54,485,486,484,487,425,58,426,420,427,454,455,453,456,59,465,57,466,461,467,53,626,625,620,627,51,646,645,641,647,52,606,605,600,607,546,49,545,540,547,560,566,50,565,567,586,48,585,581,587,703,704,701,702,309,328,188,27,142,310,329,186,28,143,311,327,187,29,141,324,308,191,26,138,325,189,24,139,306,326,307,190,25,140,300,183,334,33,133,301,184,335,34,134,302,185,333,35,132,182,303,330,32,136,30,180,304,331,137,181,305,332,31,135,670,671,676,666,219,47,92,280,12,220,45,90,281,13,221,46,91,279,14,43,218,95,276,15,44,93,277,16,216,42,217,94,278,17,225,87,38,286,18,226,88,36,287,19,227,89,37,285,20,86,224,41,282,21,283,84,222,39,22,85,223,40,284,23,663,677,678,679,1,391,389,388,390,0,395,392,393,394,2,387,385,384,386,375,3,373,372,374,379,377,376,378,4,383,5,380,381,382,6,413,415,412,414,7,416,419,417,418,8,409,411,408,410,397,9,399,396,398,401,400,10,403,402,404,11,407,405,406,684,683,682,681,123,268,340,254,245,124,269,341,252,243,125,267,339,253,244,264,122,336,257,241,265,337,255,242,120,266,121,338,256,240,129,346,274,260,251,130,347,275,258,249,131,345,273,259,250,342,128,270,263,247,261,343,126,271,248,344,127,272,262,246,673,672,667,661 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#fdf5f382e471d95c048f9fa2e9b8340aa5eb614276b1c155a6fb7129b8435eb8, 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 21:57:24 · history