Equation 677 Database

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Magma 71ac2ea4172f…

magma 71ac2ea4172f
Size
705
Isomorphism class hash
71ac2ea4172f924be74d98a8b569e2e69c846689f2620eabde2ec95f9ced90d0
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 17:25:30
Display reorder
660,489,495,115,488,490,509,515,116,508,510,529,535,114,528,530,469,475,118,461,470,430,433,119,429,431,449,455,117,448,450,113,609,615,608,610,111,629,635,628,630,112,649,655,648,650,589,109,595,588,590,549,110,555,548,550,569,108,575,568,570,689,700,688,686,481,494,6,493,492,501,514,7,513,512,520,534,8,533,532,460,474,9,473,472,434,439,10,438,426,440,454,11,453,452,4,601,614,613,612,5,621,634,633,632,3,640,654,653,652,580,1,594,593,592,541,0,554,553,552,560,2,574,573,572,692,690,695,696,363,399,49,411,303,364,400,50,412,304,365,401,48,413,305,362,398,52,410,302,360,396,53,408,300,361,397,51,409,301,55,369,405,417,309,56,370,406,418,310,54,371,407,419,311,368,58,404,416,308,366,59,402,414,306,367,57,403,415,307,678,672,665,679,291,217,103,276,15,292,218,104,277,16,293,216,102,278,17,290,220,106,279,14,288,221,107,280,12,289,219,105,281,13,101,297,223,282,21,99,298,224,283,22,100,299,222,284,23,296,97,226,285,20,294,98,227,286,18,295,96,225,287,19,666,664,676,680,480,484,83,483,496,500,504,81,503,516,521,524,82,523,536,462,465,79,464,476,423,425,80,424,427,441,444,78,443,456,74,600,604,603,616,72,620,624,623,636,73,641,644,643,656,581,77,584,583,596,540,75,544,543,556,561,76,564,563,576,701,703,699,702,497,498,230,499,491,517,518,228,519,511,538,537,229,539,531,478,477,233,479,471,420,421,231,422,432,458,457,232,459,451,236,618,617,619,611,234,637,638,639,631,235,657,658,659,651,598,239,597,599,591,557,237,558,559,551,578,238,577,579,571,693,694,691,685,482,486,139,485,487,502,506,140,505,507,522,526,138,525,527,463,467,142,466,468,435,437,143,436,428,442,446,141,445,447,137,602,606,605,607,135,622,626,625,627,136,642,646,645,647,582,133,586,585,587,542,134,546,545,547,562,132,566,565,567,687,704,697,698,168,197,32,204,184,169,195,30,205,185,170,196,31,206,183,171,193,35,207,180,172,194,33,208,181,173,192,34,209,182,27,174,203,210,190,28,175,201,211,191,29,176,202,212,189,177,26,199,213,186,178,24,200,214,187,179,25,198,215,188,669,675,681,673,315,267,85,375,256,316,268,86,376,257,317,269,84,377,255,314,266,88,374,252,312,264,89,372,253,313,265,87,373,254,91,321,273,381,262,92,322,274,382,263,90,323,275,383,261,320,94,272,380,258,318,95,270,378,259,319,93,271,379,260,663,667,684,674,44,67,125,351,387,42,68,123,352,388,43,66,124,353,389,47,70,121,350,386,45,71,122,348,384,46,69,120,349,385,131,39,65,357,393,129,40,63,358,394,130,41,64,359,395,38,127,61,356,392,36,128,62,354,390,37,126,60,355,391,683,682,677,671,243,339,163,146,327,244,340,164,144,328,245,341,162,145,329,242,338,166,149,326,240,336,167,147,324,241,337,165,148,325,161,249,345,152,333,159,250,346,150,334,160,251,347,151,335,248,157,344,155,332,246,158,342,153,330,247,156,343,154,331,670,661,668,662 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#555d8536a50144822bfea9b20f3ef68710f5792b887e6dda4840627962426043, 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 17:25:31 · history