Equation 677 Database

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Magma d6e5da605c1c…

magma d6e5da605c1c
Size
705
Isomorphism class hash
d6e5da605c1ce7a163d1d310c2d64655ee1f24ac3386e1b81563fce7a236ceb5
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 20:02:42
Display reorder
660,262,572,565,578,576,263,596,592,585,598,552,556,261,545,558,632,258,636,625,638,652,259,656,645,658,605,612,260,616,618,253,525,536,532,538,254,485,496,492,498,252,505,516,512,518,443,256,448,446,449,464,257,474,470,476,424,255,434,430,436,696,691,699,688,136,573,561,568,569,137,589,593,580,588,553,549,135,541,548,633,132,629,621,628,653,133,649,640,648,601,613,134,609,608,142,520,529,533,528,143,481,489,493,488,141,501,509,513,508,450,138,451,447,445,460,139,467,471,466,421,140,427,431,426,702,692,686,690,123,165,28,319,343,124,344,166,29,320,167,342,125,27,318,164,122,346,24,322,162,120,347,25,323,26,163,121,345,321,129,34,341,156,317,130,35,339,157,315,131,33,340,158,316,30,128,337,159,313,31,126,338,160,314,32,127,336,161,312,672,669,667,663,22,403,283,367,223,23,224,404,284,368,402,222,21,282,366,406,18,226,286,370,407,19,227,287,371,285,405,20,225,369,13,281,221,401,365,14,279,219,399,363,12,280,220,400,364,277,16,217,397,361,278,17,218,398,362,276,15,216,396,360,673,662,676,680,150,574,560,571,562,151,582,594,581,591,554,542,152,540,551,634,153,622,620,631,654,154,642,641,651,600,614,155,602,611,148,521,522,534,531,149,480,482,494,491,147,500,502,514,511,441,144,440,454,453,462,145,461,472,469,422,146,420,432,429,704,700,687,693,47,570,579,577,575,45,595,590,599,597,550,555,46,559,557,630,43,635,639,637,650,44,655,659,657,619,610,42,615,617,38,539,535,530,537,36,499,495,490,497,37,519,515,510,517,457,41,455,452,456,477,39,473,468,475,437,40,433,428,435,689,701,698,703,273,563,564,566,567,274,587,583,584,586,543,547,275,544,546,623,272,627,624,626,643,270,647,644,646,604,603,271,607,606,264,524,527,523,526,265,484,487,483,486,266,504,507,503,506,459,267,458,442,444,479,268,478,463,465,439,269,438,423,425,697,685,695,694,74,295,96,112,391,72,392,296,97,113,294,390,73,98,111,298,77,394,99,108,299,75,395,100,109,101,297,76,393,110,80,102,389,293,118,78,103,387,291,119,79,104,388,292,117,105,83,385,289,114,106,81,386,290,115,107,82,384,288,116,679,675,681,664,52,415,233,249,0,53,2,416,231,250,414,1,51,232,251,418,48,4,229,248,419,49,5,230,246,228,417,50,3,247,58,239,7,413,240,59,237,8,411,241,57,238,6,412,242,235,54,10,409,243,236,55,11,410,244,234,56,9,408,245,684,678,671,682,207,172,181,379,355,208,356,173,182,380,171,354,209,180,378,168,206,358,184,382,169,204,359,185,383,183,170,205,357,381,213,187,353,178,377,214,188,351,179,375,215,186,352,177,376,190,212,349,174,373,191,210,350,175,374,189,211,348,176,372,674,683,677,670,193,331,307,94,67,194,68,332,308,95,330,66,192,306,93,334,196,70,310,90,335,197,71,311,91,309,333,195,69,92,199,305,65,329,85,200,303,63,327,86,198,304,64,328,84,301,202,61,325,88,302,203,62,326,89,300,201,60,324,87,661,665,666,668 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#b87a44718af64d04bd4c9a05b8565b67306fb6d5f63754d3fbad663d9bf67702, 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 20:02:43 · history