Equation 677 Database

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Magma 44b339a3e06e…

magma 44b339a3e06e
Size
705
Isomorphism class hash
44b339a3e06e71143f26cc056165b33c608475178a473cf51af97b31cf11737d
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 15:16:58
Display reorder
660,256,568,602,591,586,569,257,600,592,587,601,567,593,585,255,605,252,564,590,582,253,603,565,588,583,254,604,566,589,584,608,574,262,597,577,606,575,263,598,578,607,573,261,599,576,596,570,611,258,580,571,609,259,594,581,572,610,260,595,579,687,688,686,685,327,61,51,47,81,62,328,52,45,82,53,60,46,83,329,50,326,64,43,80,324,48,65,44,78,325,49,63,42,79,57,67,333,38,72,58,68,334,36,73,59,66,335,37,74,41,70,56,332,75,71,54,330,39,76,69,55,331,40,77,703,704,701,702,99,517,552,543,538,518,100,553,544,539,554,516,545,537,101,555,98,520,542,534,96,556,521,540,535,97,557,519,541,536,558,523,105,549,529,559,524,106,550,530,560,522,107,551,528,548,526,561,104,532,527,562,102,546,533,525,563,103,547,531,671,672,670,669,32,383,364,359,338,381,30,365,357,336,363,382,358,337,31,360,35,379,355,341,33,361,380,356,339,34,362,378,354,340,370,374,27,350,344,371,372,28,348,342,369,373,29,349,343,353,377,366,26,347,375,367,24,351,345,376,368,25,352,346,679,680,678,677,395,190,172,206,195,191,393,173,204,196,171,189,205,197,394,168,391,186,209,194,392,169,187,207,192,390,170,188,208,193,178,181,386,212,201,179,182,384,210,202,177,180,385,211,203,215,184,174,389,200,185,175,387,213,198,183,176,388,214,199,692,691,690,689,244,477,460,455,433,478,245,461,453,434,459,479,454,432,243,456,240,476,451,436,241,457,474,452,437,242,458,475,450,435,466,468,250,446,439,467,469,251,444,440,465,470,249,445,438,449,471,462,246,442,472,463,247,447,443,473,464,248,448,441,699,700,698,697,109,167,146,137,131,165,110,144,135,129,145,166,136,130,108,149,112,163,133,127,113,147,164,134,128,111,148,162,132,126,152,158,115,143,122,150,156,116,141,120,151,157,114,142,121,139,161,155,118,125,159,153,119,140,123,160,154,117,138,124,663,664,662,661,270,638,627,619,220,636,271,628,620,221,629,637,618,219,272,626,273,641,622,216,274,624,639,623,217,275,625,640,621,218,633,644,268,617,226,634,642,269,615,227,635,643,267,616,225,613,647,632,264,222,645,630,265,614,223,646,631,266,612,224,682,683,684,681,86,508,505,491,480,509,84,506,489,481,504,507,490,482,85,656,89,659,658,657,87,649,650,648,651,88,654,655,652,653,499,514,92,494,486,500,515,90,492,487,498,513,91,493,488,497,510,502,95,485,511,503,93,495,483,512,501,94,496,484,695,696,693,694,5,403,13,430,412,404,3,14,431,413,12,402,429,411,4,16,0,406,426,408,2,17,407,427,409,1,15,405,428,410,19,401,11,421,418,20,399,9,422,419,18,400,10,420,417,424,397,22,7,414,398,23,8,425,415,396,21,6,423,416,667,668,665,666,231,299,278,312,305,297,232,276,313,303,277,298,314,304,233,281,230,295,315,301,228,279,296,316,302,229,280,294,317,300,284,290,237,318,311,282,288,238,319,309,283,289,239,320,310,321,293,287,236,307,291,285,234,322,308,292,286,235,323,306,675,676,673,674 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#101de34e785e3f92e4e627a1da3ddc1fe7ebde0c6c88cd6039e0733ba8ec0ae0, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 15:16:59 · history