Equation 677 Database

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Magma 35938a03dd26…

magma 35938a03dd26
Size
705
Isomorphism class hash
35938a03dd26112c31164b3cce905fcd3266cb8f5996651a58bb54102c12138e
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 15:10:08
Display reorder
660,562,577,126,572,571,127,582,592,591,597,128,557,542,552,551,622,129,637,632,631,642,130,657,652,651,602,131,617,612,611,124,537,532,522,531,125,497,492,482,491,123,517,512,502,511,449,120,447,442,446,475,121,472,462,471,422,435,122,432,431,696,686,689,691,560,564,232,565,574,233,580,585,594,584,231,544,540,545,554,621,228,624,625,634,641,229,644,645,654,600,230,604,605,614,238,524,525,520,534,239,484,485,481,494,237,504,505,500,514,450,234,451,440,448,464,235,465,461,474,420,424,236,425,434,702,693,694,690,57,259,205,179,391,206,58,177,392,260,204,258,59,178,390,56,208,262,175,394,54,209,263,176,395,55,207,261,174,393,211,257,170,48,389,212,255,168,49,387,210,256,169,50,388,253,214,173,51,385,254,215,171,52,386,53,252,213,172,384,661,680,674,676,153,271,76,343,295,77,154,344,296,272,75,270,155,342,294,152,72,274,346,298,150,73,275,347,299,151,74,273,345,297,82,269,341,144,293,83,267,339,145,291,81,268,340,146,292,265,78,337,147,289,266,79,338,148,290,149,264,80,336,288,663,677,666,670,568,563,3,567,578,4,588,587,598,583,5,543,548,547,558,628,2,623,627,638,648,1,643,647,658,608,0,603,607,618,9,523,527,528,538,10,483,487,488,498,11,503,507,508,518,443,8,444,453,456,463,6,467,468,476,428,423,7,427,436,704,688,699,697,579,570,25,566,573,26,599,586,593,590,24,550,559,546,553,639,28,630,626,633,659,29,650,646,653,619,27,610,606,613,31,530,526,539,533,32,490,486,499,493,30,510,506,519,513,454,34,452,457,455,470,35,466,477,473,437,430,33,426,433,698,701,692,703,561,576,20,575,569,18,581,595,589,596,19,556,541,555,549,620,23,636,635,629,640,21,656,655,649,601,22,616,615,609,15,536,535,521,529,16,496,495,480,489,17,516,515,501,509,458,14,459,441,445,479,12,478,460,469,421,439,13,438,429,695,700,687,685,37,250,222,319,379,223,38,320,380,251,224,249,36,318,378,40,225,246,322,382,41,226,247,323,383,39,227,248,321,381,220,241,317,43,377,221,242,315,44,375,219,240,316,42,376,244,216,313,46,373,245,217,314,47,374,45,243,218,312,372,679,665,673,668,142,116,66,355,88,67,143,356,89,114,68,115,141,354,87,138,69,119,358,84,139,70,117,359,85,140,71,118,357,86,64,111,353,133,94,65,112,351,134,95,63,113,352,132,93,110,60,349,136,90,108,61,350,137,91,135,109,62,348,92,684,662,682,671,192,331,163,190,307,164,193,191,308,332,162,330,194,189,306,195,166,334,186,310,196,167,335,187,311,197,165,333,188,309,161,329,181,198,305,159,327,182,199,303,160,328,180,200,304,325,157,184,201,301,326,158,185,202,302,203,324,156,183,300,669,683,667,681,403,367,96,415,284,97,404,416,282,368,98,366,402,414,283,406,99,370,418,287,407,100,371,419,285,405,101,369,417,286,102,365,413,401,279,103,363,411,399,280,104,364,412,400,281,361,105,409,397,278,362,106,410,398,276,396,360,107,408,277,672,675,664,678 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#06e28404eb43925716bfc8e4d73e8cc7ccb918742e903c176b52de636b48f456, 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 15:10:09 · history