Equation 677 Database

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Magma 09ec42e9e9e7…

magma 09ec42e9e9e7
Size
705
Isomorphism class hash
09ec42e9e9e71f349055c8c1e2e6e412dce258d97525ad52facec5e5882206e0
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 20:31:01
Display reorder
660,293,603,326,318,305,327,294,316,306,601,325,602,292,317,304,599,329,289,314,301,600,330,290,315,302,598,328,291,313,303,332,299,594,324,311,322,333,300,592,312,331,298,593,323,310,295,335,597,320,307,296,336,595,321,308,297,334,596,319,309,687,688,686,685,239,171,226,381,204,227,240,379,202,169,228,170,238,380,203,174,225,235,384,200,172,223,236,382,201,173,224,237,383,199,217,230,177,376,195,377,218,231,175,193,219,229,176,378,194,233,220,180,375,198,234,221,178,373,196,232,222,179,374,197,703,704,701,702,572,277,556,549,584,557,573,547,585,278,558,279,571,548,583,280,559,568,545,580,281,560,569,546,581,282,561,570,544,582,562,578,283,555,590,553,563,579,284,591,564,577,285,554,589,574,565,286,551,586,575,566,287,552,587,576,567,288,550,588,671,672,670,669,41,98,164,391,248,165,42,392,249,99,163,97,40,393,247,101,167,37,394,251,102,168,38,395,252,100,166,39,396,250,162,47,104,389,246,390,160,48,105,244,161,46,103,388,245,43,158,107,385,242,44,159,108,386,243,45,157,106,387,241,679,680,678,677,413,255,398,433,426,399,414,434,424,253,397,254,412,435,425,258,401,409,436,422,256,402,410,437,423,257,400,411,438,421,404,419,261,439,432,440,405,420,259,430,403,418,260,441,431,415,407,264,442,428,416,408,262,443,429,417,406,263,444,427,692,691,690,689,73,115,66,49,499,64,74,50,500,116,65,117,75,51,501,118,62,76,52,502,119,63,77,53,503,120,61,78,54,504,72,79,113,55,497,56,70,80,114,498,71,81,112,57,496,82,68,109,58,493,83,69,110,59,494,84,67,111,60,495,699,700,698,697,128,34,12,23,134,10,129,24,135,35,11,36,127,22,133,33,8,131,19,137,31,9,132,20,138,32,7,130,21,136,3,126,25,14,140,15,0,124,26,141,2,125,27,13,139,122,6,28,17,143,123,4,29,18,144,121,5,30,16,142,663,664,662,661,612,339,642,633,617,640,610,631,618,337,641,338,611,632,616,342,645,615,629,620,340,643,613,630,621,341,644,614,628,619,648,607,345,639,623,637,646,608,343,624,647,609,344,638,622,606,651,348,635,626,604,649,346,636,627,605,650,347,634,625,682,683,684,681,527,90,516,511,535,517,525,512,536,88,515,89,526,513,537,86,1,524,514,534,87,653,654,652,655,85,657,658,656,659,522,533,96,509,541,510,523,531,94,542,521,532,95,508,543,529,518,92,505,540,530,519,93,506,538,528,520,91,507,539,695,696,693,694,462,265,446,485,470,447,460,486,471,266,445,267,461,484,469,268,449,458,481,473,269,450,459,482,474,270,448,457,483,472,452,468,271,491,476,492,453,466,272,477,451,467,273,490,475,464,455,274,487,479,465,456,275,488,480,463,454,276,489,478,667,668,665,666,357,185,148,205,363,149,355,206,361,186,150,184,356,207,362,181,147,360,208,366,182,145,358,209,364,183,146,359,210,365,154,352,191,211,369,212,155,353,192,367,156,354,190,213,368,351,153,187,214,372,349,151,188,215,370,350,152,189,216,371,675,676,673,674 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#be22598f61f867b223264cf52ecf408910eea148415a700aef96392fba43b30a, 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 20:31:03 · history