Equation 677 Database

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Magma b5ab34bacd18…

magma b5ab34bacd18
Size
705
Isomorphism class hash
b5ab34bacd189b8f08cea03179a979d31cee4609b594eafc681834d5bfdfcc4f
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 19:42:15
Display reorder
660,527,538,64,521,531,487,65,480,491,498,507,518,63,501,511,455,449,60,448,450,475,466,61,461,468,435,426,62,420,428,70,647,658,640,651,71,607,618,600,611,69,627,638,620,631,567,66,578,560,571,587,67,598,580,591,547,68,558,540,551,696,691,689,701,522,536,121,529,526,482,122,489,486,496,502,516,120,509,506,453,440,124,444,443,473,460,125,467,465,433,421,123,427,425,127,642,656,649,646,128,602,616,609,606,126,622,636,629,626,562,130,576,569,566,582,131,596,589,586,542,129,556,549,546,700,687,686,697,172,281,40,144,191,173,41,145,189,279,171,280,39,146,190,277,168,36,147,187,278,169,37,148,188,276,170,38,149,186,46,178,287,150,182,47,179,285,151,180,45,177,286,152,181,174,42,283,153,185,175,43,284,154,183,176,44,282,155,184,674,666,670,664,401,95,113,389,3,399,111,387,4,93,400,94,112,388,5,91,397,109,385,2,92,398,110,386,1,90,396,108,384,0,119,407,86,395,9,117,405,84,393,10,118,406,85,394,11,403,115,89,391,8,404,116,87,392,6,402,114,88,390,7,681,675,682,683,523,530,132,532,534,483,133,492,494,490,503,510,134,512,514,456,447,135,451,452,478,462,136,469,471,436,422,137,429,431,138,643,650,652,654,139,603,610,612,614,140,623,630,632,634,563,141,570,572,574,583,142,590,592,594,543,143,550,552,554,692,703,694,702,520,537,80,528,539,481,78,488,499,497,500,517,79,508,519,454,458,83,457,459,474,477,81,476,479,434,438,82,437,439,75,641,657,648,659,76,601,617,608,619,77,621,637,628,639,561,74,577,568,579,581,72,597,588,599,541,73,557,548,559,688,690,698,699,533,525,96,524,535,493,97,484,495,485,513,505,98,504,515,442,445,99,441,446,464,470,100,463,472,424,430,101,423,432,102,653,645,644,655,103,613,605,604,615,104,633,625,624,635,573,105,565,564,575,593,106,585,584,595,553,107,545,544,555,704,695,693,685,245,377,160,269,261,243,161,267,262,375,244,376,159,268,263,373,241,156,265,260,374,242,157,266,258,372,240,158,264,259,166,251,383,275,252,167,249,381,273,253,165,250,382,274,254,247,162,379,271,255,248,163,380,272,256,246,164,378,270,257,663,680,661,678,317,413,50,236,35,315,48,234,33,411,316,412,49,235,34,409,313,53,239,31,410,314,51,237,32,408,312,52,238,30,56,323,419,231,26,54,321,417,232,24,55,322,418,233,25,319,59,415,230,29,320,57,416,228,27,318,58,414,229,28,672,679,668,684,341,293,202,329,353,339,203,327,351,291,340,292,201,328,352,289,337,198,325,349,290,338,199,326,350,288,336,200,324,348,193,347,299,335,359,194,345,297,333,357,192,346,298,334,358,343,196,295,331,355,344,197,296,332,356,342,195,294,330,354,669,676,673,665,220,210,16,305,365,221,17,303,363,211,219,212,15,304,364,213,216,12,301,361,214,217,13,302,362,215,218,14,300,360,22,226,208,311,371,23,227,209,309,369,21,225,207,310,370,222,18,204,307,367,223,19,205,308,368,224,20,206,306,366,667,677,671,662 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#a3dbb2a8d5932ce23601e140d077e70c3bff24b108fb14183b80120946e543a6, 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 19:42:16 · history