Equation 677 Database

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Magma a3a934c0dc3c…

magma a3a934c0dc3c
Size
705
Isomorphism class hash
a3a934c0dc3c4d6e1b6fb845e1efffde4d9dc0f560f339ffedaad2e257e25417
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 16:46:28
Display reorder
660,142,141,143,140,138,139,132,133,134,135,136,137,159,58,59,160,57,161,54,158,55,156,56,157,49,165,50,166,48,167,52,164,53,162,51,163,125,149,123,147,124,148,121,145,122,146,120,144,131,155,129,153,130,154,127,151,128,152,126,150,687,699,694,704,604,603,605,602,600,601,609,610,611,608,606,607,590,471,472,588,473,589,470,593,468,591,469,592,477,596,478,594,479,595,476,599,474,597,475,598,581,575,579,573,580,574,577,571,578,572,576,570,587,566,585,564,586,565,583,569,584,567,582,568,685,696,693,700,488,487,486,490,491,489,485,483,484,481,482,480,527,93,94,525,95,526,92,523,90,524,91,522,84,518,85,516,86,517,87,521,88,519,89,520,560,492,558,493,559,494,563,495,561,496,562,497,555,498,556,499,557,500,554,501,552,502,553,503,667,676,663,682,352,351,353,350,348,349,357,358,359,356,354,355,336,97,98,337,96,338,100,339,101,340,99,341,103,342,104,343,102,344,106,345,107,346,105,347,328,362,329,360,327,361,324,365,325,363,326,364,334,368,335,366,333,367,330,371,331,369,332,370,670,675,664,681,455,454,453,450,451,452,445,446,444,448,449,447,440,14,12,438,13,439,17,443,15,441,16,442,20,435,18,436,19,437,23,434,21,432,22,433,427,467,428,465,426,466,430,463,431,464,429,462,425,458,423,456,424,457,421,461,422,459,420,460,686,697,690,701,281,280,279,276,277,278,286,287,285,282,283,284,323,42,43,321,44,322,45,319,46,320,47,318,40,314,41,312,39,313,36,317,37,315,38,316,303,289,304,290,305,288,302,292,300,293,301,291,309,295,310,296,311,294,308,298,306,299,307,297,688,698,692,702,257,256,255,252,253,254,262,263,261,258,259,260,242,119,117,240,118,241,115,245,116,243,114,244,110,248,108,246,109,247,113,251,111,249,112,250,236,266,234,264,235,265,239,269,237,267,238,268,231,272,232,270,233,271,230,275,228,273,229,274,689,695,691,703,407,406,405,402,403,404,397,398,396,400,401,399,392,4,5,390,3,391,1,395,0,393,2,394,10,387,11,388,9,389,6,386,7,384,8,385,372,417,373,418,374,419,375,416,376,414,377,415,378,408,379,409,380,410,381,411,382,412,383,413,671,677,665,679,169,168,170,171,172,173,174,175,176,177,178,179,544,34,35,545,33,543,30,540,31,541,32,542,25,550,26,551,24,549,28,546,29,547,27,548,534,509,535,507,536,508,537,505,538,506,539,504,532,515,533,513,531,514,528,511,529,512,530,510,668,673,662,683,645,647,646,643,644,642,638,636,637,641,639,640,630,82,83,631,81,632,78,633,79,634,80,635,73,628,74,629,72,627,76,624,77,625,75,626,619,654,620,655,618,656,622,657,623,658,621,659,617,652,615,653,616,651,613,648,614,649,612,650,669,674,661,684,203,202,201,198,199,200,193,194,192,196,197,195,187,67,68,188,66,186,70,190,71,191,69,189,65,185,63,183,64,184,61,181,62,182,60,180,221,215,219,213,220,214,217,211,218,212,216,210,227,206,225,204,226,205,223,209,224,207,222,208,666,678,672,680 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {62} 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 16:46:29 · history