Equation 677 Database

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Magma 00d2b840bc57…

magma 00d2b840bc57
Size
705
Isomorphism class hash
00d2b840bc579ec3d2ee7d4fbc1161b8a0c6bc515b5bfadd12b0a51929a69ae0
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 21:21:37
Display reorder
660,643,71,647,648,641,607,69,603,608,600,623,627,628,70,621,567,563,67,568,560,587,583,68,588,580,547,543,66,548,540,463,468,467,62,460,423,427,426,60,422,443,448,447,61,442,528,523,527,65,522,488,483,487,63,482,508,503,507,64,502,703,688,692,687,658,258,652,646,645,612,259,618,606,605,638,632,626,260,625,572,578,261,566,565,592,598,262,586,585,552,558,263,546,545,478,466,472,256,465,436,425,431,257,424,458,446,452,255,445,526,538,532,252,525,486,498,492,253,485,506,518,512,254,505,694,700,702,704,271,113,247,92,383,248,111,272,90,381,270,246,91,112,382,250,274,109,95,379,251,275,110,93,380,249,273,108,94,378,269,87,245,119,374,267,88,243,117,372,268,89,244,118,373,86,265,241,115,377,84,266,242,116,375,85,264,240,114,376,665,669,675,673,203,127,407,183,306,405,128,201,184,307,202,406,185,126,308,403,199,130,182,309,404,200,131,180,310,402,198,129,181,311,194,189,398,125,304,192,190,396,123,305,193,191,397,124,303,188,197,401,121,300,186,195,399,122,301,187,196,400,120,302,664,677,667,668,651,229,640,644,653,601,230,611,604,613,631,620,624,228,633,561,571,232,564,573,581,591,233,584,593,541,551,231,544,553,471,464,461,235,473,430,438,437,236,439,451,444,441,234,453,524,531,521,238,533,484,491,481,239,493,504,511,501,237,513,698,686,696,685,659,289,655,657,650,615,290,619,617,610,639,635,637,288,630,575,579,292,577,570,595,599,293,597,590,555,559,291,557,550,479,477,475,295,470,420,435,433,296,429,459,457,455,294,450,537,539,535,298,530,497,499,495,299,490,517,519,515,297,510,701,695,690,697,654,47,649,642,656,609,45,614,602,616,634,629,622,46,636,569,574,43,562,576,589,594,44,582,596,549,554,42,542,556,474,462,469,38,476,432,421,428,36,434,454,440,449,37,456,520,534,529,41,536,480,494,489,39,496,500,514,509,40,516,691,689,699,693,419,79,169,395,347,170,80,417,393,345,418,168,394,78,346,172,415,82,391,343,173,416,83,392,344,171,414,81,390,342,410,386,175,77,338,408,384,176,75,336,409,385,174,76,337,389,413,178,73,341,387,411,179,74,339,388,412,177,72,340,684,681,670,679,285,100,9,323,335,10,101,286,321,333,287,11,322,99,334,8,284,96,319,331,6,282,97,320,332,7,283,98,318,330,276,314,1,106,326,277,312,0,107,324,278,313,2,105,325,317,279,3,102,329,315,280,4,103,327,316,281,5,104,328,661,676,663,683,371,205,359,153,135,357,206,369,154,136,370,358,155,204,137,355,367,208,152,134,356,368,209,150,132,354,366,207,151,133,362,144,350,211,141,360,145,348,212,142,361,146,349,210,143,147,365,353,214,140,148,363,351,215,138,149,364,352,213,139,662,671,666,674,158,55,34,224,15,35,56,156,222,16,157,33,223,54,17,30,161,58,227,14,31,159,59,225,12,32,160,57,226,13,164,219,25,53,21,162,220,26,51,22,163,221,24,52,23,218,167,28,49,20,216,165,29,50,18,217,166,27,48,19,672,678,682,680 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#eb741fb6db55479c3e56ca4f84f09a48d9f1cbf15ed347cc0747015cb842acab, 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 21:21:38 · history