Equation 677 Database

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Magma 77fe259a12fb…

magma 77fe259a12fb
Size
705
Isomorphism class hash
77fe259a12fb7990a30585850f34702e0380431316c50367325eddb799190335
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 20:34:40
Display reorder
660,538,71,535,520,531,495,498,481,491,69,515,70,518,501,511,67,454,455,449,453,68,472,475,461,469,66,432,435,421,429,658,655,62,640,651,618,615,60,601,611,638,635,61,620,631,575,578,65,561,571,595,598,63,581,591,541,555,558,64,551,686,688,701,696,537,161,528,527,521,488,497,487,480,159,508,160,517,507,500,157,443,447,442,441,158,468,474,467,466,156,428,434,427,426,657,648,167,647,646,617,608,165,607,606,637,628,166,627,626,568,577,163,567,566,588,597,164,587,586,547,548,557,162,546,694,692,700,695,1,170,192,269,281,193,0,267,279,168,194,169,2,268,280,173,195,3,265,277,171,196,4,266,278,172,197,5,264,276,6,198,176,275,287,7,199,174,273,285,8,200,175,274,286,201,9,179,271,283,202,10,177,272,284,270,203,11,178,282,666,667,668,664,317,26,377,365,401,375,315,363,399,24,376,25,316,364,400,29,373,313,361,397,27,374,314,362,398,28,372,312,360,396,323,383,32,371,407,321,381,30,369,405,322,382,31,370,406,379,319,35,367,403,380,320,33,368,404,366,378,318,34,402,677,682,672,678,523,102,522,525,524,482,483,485,484,103,502,104,503,505,504,105,448,450,452,451,106,460,462,464,463,107,420,422,424,423,642,641,100,644,643,602,600,101,604,603,622,621,99,624,623,560,562,96,564,563,580,582,97,584,583,544,540,542,98,543,698,703,702,697,530,108,529,534,539,489,490,494,499,109,509,110,510,514,519,111,457,456,458,459,112,477,476,478,479,113,437,436,438,439,650,649,114,654,659,610,609,115,614,619,630,629,116,634,639,569,570,117,574,579,589,590,118,594,599,554,549,550,119,559,693,689,685,687,536,77,533,526,532,493,496,486,492,75,513,76,516,506,512,73,445,446,440,444,74,471,473,465,470,72,431,433,425,430,656,653,83,645,652,616,613,81,605,612,636,633,82,625,632,573,576,79,565,572,593,596,80,585,592,545,553,556,78,552,704,690,699,691,293,150,329,16,123,327,291,17,124,151,328,152,292,15,125,153,325,289,12,122,154,326,290,13,120,155,324,288,14,121,299,335,148,22,129,297,333,149,23,130,298,334,147,21,131,331,295,144,18,128,332,296,145,19,126,20,330,294,146,127,681,676,669,673,353,43,413,215,305,411,351,213,303,44,412,42,352,214,304,46,409,349,211,301,47,410,350,212,302,45,408,348,210,300,359,419,41,206,311,357,417,39,204,309,358,418,40,205,310,415,355,37,209,307,416,356,38,207,308,208,414,354,36,306,679,670,675,684,237,188,389,257,245,387,238,255,243,186,388,187,239,256,244,191,385,236,253,241,189,386,234,254,242,190,384,235,252,240,228,395,183,263,251,229,393,184,261,249,230,394,185,262,250,391,231,182,259,247,392,232,180,260,248,258,390,233,181,246,665,663,662,680,54,136,226,88,341,227,55,89,339,137,225,135,56,87,340,132,222,57,84,337,133,223,58,85,338,134,224,59,86,336,52,217,142,94,347,53,218,143,95,345,51,216,141,93,346,220,48,138,90,343,221,49,139,91,344,92,219,50,140,342,683,674,671,661 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#c633edfa20dc6722982152bc303db7386181f99f3fbdfeb33272ccd5420b69f5, 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 20:34:41 · history