Equation 677 Database

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Magma ddaece32fe3b…

magma ddaece32fe3b
Size
705
Isomorphism class hash
ddaece32fe3b5c323c7ef6f8f6bbaa5a702f648a5f57128b6b985c98bdc27326
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 18:06:55
Display reorder
660,440,454,450,73,442,460,74,474,470,462,420,72,435,432,426,76,500,514,510,502,77,521,534,530,522,75,480,494,490,482,577,560,572,79,561,597,580,592,80,581,557,541,552,78,540,621,637,632,82,620,657,640,652,83,641,601,617,612,81,600,698,690,696,688,448,443,446,122,444,468,120,463,466,464,422,121,427,429,428,125,508,503,506,504,123,528,523,526,524,124,488,483,486,484,565,570,568,128,566,585,590,588,126,586,545,550,548,127,546,630,625,628,131,626,645,650,648,129,646,610,605,608,130,606,701,694,703,685,349,135,397,209,337,350,207,136,398,338,348,208,137,396,336,205,352,134,400,340,206,353,132,401,341,204,351,133,399,339,141,355,403,215,343,142,356,404,213,344,143,354,402,214,342,358,140,406,211,346,138,359,407,212,347,357,139,405,210,345,668,682,673,670,22,361,165,254,409,23,252,362,166,410,21,253,360,167,408,257,18,364,164,412,255,19,365,162,413,256,20,363,163,411,367,13,156,260,415,368,14,157,258,416,366,12,158,259,414,16,370,159,263,418,371,17,160,261,419,15,369,161,262,417,684,680,672,664,441,456,458,110,457,461,108,477,478,476,425,109,437,438,436,113,501,517,518,516,111,520,538,539,537,112,481,497,498,496,564,562,574,116,563,584,582,594,114,583,544,542,554,115,543,622,624,634,119,623,644,642,654,117,643,602,604,614,118,603,687,692,699,697,459,452,447,58,451,479,59,472,467,471,439,57,434,430,433,54,519,512,507,511,55,536,532,527,531,56,499,492,487,491,575,579,569,49,573,595,599,589,50,593,555,559,549,48,553,639,635,629,52,633,655,659,649,53,653,619,615,609,51,613,691,702,693,704,449,445,455,63,453,469,64,465,475,473,431,65,421,424,423,62,509,505,515,513,60,529,525,535,533,61,489,485,495,493,567,571,578,69,576,587,591,598,70,596,547,551,558,71,556,631,627,638,68,636,647,651,658,66,656,611,607,618,67,616,695,700,686,689,154,200,325,103,373,155,104,198,326,374,153,102,199,324,372,106,150,203,328,376,107,151,201,329,377,105,152,202,327,375,195,145,331,101,379,196,146,332,99,380,197,144,330,100,378,148,194,334,97,382,192,149,335,98,383,147,193,333,96,381,676,661,674,678,226,239,385,95,249,227,93,237,386,250,225,94,238,384,251,91,222,235,388,248,92,223,236,389,246,90,224,234,387,247,230,217,391,86,240,228,218,392,84,241,229,216,390,85,242,220,233,394,89,243,231,221,395,87,244,219,232,393,88,245,666,681,667,663,174,43,1,265,27,175,266,44,0,28,176,264,42,2,29,268,177,46,3,26,269,178,47,4,24,267,179,45,5,25,41,172,6,271,33,39,173,7,272,34,40,171,8,270,35,168,37,9,274,32,38,169,10,275,30,170,36,11,273,31,675,679,669,662,313,280,305,181,292,314,182,281,303,293,312,180,279,304,291,184,316,276,301,288,185,317,277,302,289,183,315,278,300,290,286,319,311,187,298,287,320,309,188,299,285,318,310,186,297,322,282,307,190,294,283,323,308,191,295,321,284,306,189,296,683,665,677,671 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#62fadf6abad0ff7e327687381d1d05b120aac2dcda3d9647c53ea471472f147e, 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 18:06:56 · history