Equation 677 Database

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Magma 26aa1ff407b2…

magma 26aa1ff407b2
Size
705
Isomorphism class hash
26aa1ff407b22ff2a5e00b3dcae5873c4dfeb2ee766fa739b078093055b96106
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 21:49:46
Display reorder
660,580,579,581,578,576,577,585,586,587,584,582,583,656,654,655,659,657,658,651,652,653,650,648,649,168,169,170,171,172,173,174,175,176,177,178,179,627,628,629,626,624,625,633,634,635,632,630,631,601,602,600,604,605,603,607,608,606,610,611,609,681,702,691,701,208,207,209,206,204,205,213,214,215,212,210,211,399,400,401,398,396,397,405,406,407,404,402,403,96,97,98,99,100,101,102,103,104,105,106,107,275,273,274,271,272,270,266,264,265,269,267,268,480,481,482,483,484,485,486,487,488,489,490,491,682,703,700,692,373,372,374,375,376,377,378,379,380,381,382,383,317,315,316,313,314,312,323,321,322,319,320,318,342,343,344,345,346,347,340,341,339,336,337,338,355,356,354,358,359,357,353,351,352,349,350,348,0,2,1,4,5,3,7,8,6,10,11,9,665,684,674,683,644,643,642,646,647,645,641,639,640,637,638,636,613,614,612,616,617,615,619,620,618,622,623,621,575,573,574,571,572,570,566,564,565,569,567,568,29,27,28,25,26,24,35,33,34,31,32,30,595,596,594,598,599,597,593,591,592,589,590,588,663,689,677,668,203,202,201,198,199,200,193,194,192,196,197,195,293,291,292,289,290,288,299,297,298,295,296,294,450,451,452,453,454,455,448,449,447,444,445,446,420,421,422,423,424,425,426,427,428,429,430,431,560,558,559,563,561,562,555,556,557,554,552,553,680,704,699,696,507,509,508,505,506,504,515,513,514,511,512,510,300,301,302,303,304,305,306,307,308,309,310,311,536,534,535,539,537,538,531,532,533,530,528,529,131,129,130,127,128,126,122,120,121,125,123,124,229,230,228,232,233,231,235,236,234,238,239,237,678,695,697,694,332,331,330,334,335,333,329,327,328,325,326,324,132,133,134,135,136,137,138,139,140,141,142,143,386,384,385,389,387,388,392,390,391,395,393,394,119,117,118,115,116,114,110,108,109,113,111,112,371,369,370,367,368,366,362,360,361,365,363,364,679,693,698,690,63,65,64,61,62,60,71,69,70,67,68,66,263,261,262,259,260,258,254,252,253,257,255,256,154,155,153,150,151,152,145,146,144,148,149,147,166,167,165,162,163,164,157,158,156,160,161,159,50,48,49,53,51,52,56,54,55,59,57,58,666,686,667,669,278,277,276,280,281,279,283,284,282,286,287,285,180,181,182,183,184,185,186,187,188,189,190,191,469,470,468,472,473,471,475,476,474,478,479,477,12,13,14,15,16,17,18,19,20,21,22,23,416,414,415,419,417,418,411,412,413,410,408,409,662,688,675,671,456,458,457,461,459,460,464,462,463,467,465,466,436,437,435,432,433,434,442,443,441,438,439,440,548,546,547,551,549,550,543,544,545,542,540,541,44,42,43,47,45,46,39,40,41,38,36,37,90,91,92,93,94,95,88,89,87,84,85,86,661,685,672,676,73,72,74,75,76,77,78,79,80,81,82,83,498,499,500,501,502,503,496,497,495,492,493,494,220,221,219,216,217,218,226,227,225,222,223,224,249,250,251,248,246,247,240,241,242,243,244,245,523,524,522,526,527,525,521,519,520,517,518,516,664,687,673,670 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {63} 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 21:49:47 · history