Equation 677 Database

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Magma 50eba8fa6d7c…

magma 50eba8fa6d7c
Size
705
Isomorphism class hash
50eba8fa6d7c4cee57fa5b2f36b6e608d7a227c9d0bfb2105d68c50e867ad4d6
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 19:12:58
Display reorder
660,496,488,483,230,490,228,516,508,503,510,528,229,536,523,530,233,476,468,464,470,231,433,431,428,432,232,456,448,444,450,616,608,603,236,610,636,628,623,234,630,656,647,642,235,649,598,588,583,239,590,558,548,543,237,550,578,568,563,238,570,689,693,687,686,493,481,495,17,480,15,513,501,515,500,521,16,533,535,520,13,473,462,475,460,14,437,434,439,423,12,453,442,455,440,613,601,615,23,600,633,620,635,21,621,652,640,655,22,641,593,581,597,19,580,553,541,557,20,540,573,561,577,18,560,685,691,688,701,26,327,116,97,375,98,24,328,114,376,329,96,25,115,377,100,29,326,119,374,101,27,324,117,372,99,28,325,118,373,32,333,111,103,381,30,334,112,104,382,31,335,113,102,383,35,332,110,106,380,33,330,108,107,378,34,331,109,105,379,665,670,677,676,152,60,266,293,45,291,150,61,264,46,62,292,151,265,47,289,155,63,269,44,290,153,64,267,42,288,154,65,268,43,147,66,272,299,36,148,67,270,297,37,149,68,271,298,38,146,69,275,295,39,144,70,273,296,40,145,71,274,294,41,672,674,661,668,491,482,492,121,489,122,511,502,512,509,522,120,531,532,529,124,471,463,472,469,125,426,424,427,425,123,451,443,452,449,611,602,612,127,609,631,622,632,128,629,650,653,651,126,648,591,582,592,130,589,551,542,552,131,549,571,562,572,129,569,700,690,692,695,499,498,497,174,484,175,519,518,517,504,537,176,539,538,524,177,479,477,478,461,178,422,421,420,429,179,459,457,458,441,619,618,617,172,604,637,638,639,173,624,659,657,658,171,643,599,594,595,168,584,559,554,555,169,544,579,574,575,170,564,694,697,704,699,494,487,486,6,485,7,514,507,506,505,527,8,534,526,525,9,474,467,466,465,10,438,436,435,430,11,454,447,446,445,614,607,606,4,605,634,627,626,5,625,654,646,645,3,644,596,587,586,1,585,556,547,546,0,545,576,567,566,2,565,698,696,702,703,363,280,306,52,402,53,364,281,307,404,279,51,365,308,407,48,362,276,309,401,49,360,277,310,396,50,361,278,311,399,369,286,304,58,414,370,287,305,59,417,371,285,303,57,419,368,282,300,54,413,366,283,301,55,408,367,284,302,56,411,684,681,669,679,204,189,219,94,203,95,205,190,220,201,191,93,206,221,202,90,207,188,218,199,91,208,186,216,200,92,209,187,217,198,210,180,225,85,194,211,181,226,86,192,212,182,227,84,193,213,183,224,88,197,214,184,222,89,195,215,185,223,87,196,678,671,680,683,387,240,351,158,255,156,388,241,352,256,242,157,389,353,257,161,386,243,350,254,159,384,244,348,252,160,385,245,349,253,393,246,357,164,261,394,247,358,162,262,395,248,359,163,263,392,249,356,167,260,390,250,354,165,258,391,251,355,166,259,663,675,673,667,403,339,315,132,77,133,405,340,316,75,341,134,406,317,76,135,400,338,314,73,136,397,336,312,74,137,398,337,313,72,415,345,321,138,83,416,346,322,139,81,418,347,323,140,82,412,344,320,141,79,409,342,318,142,80,410,343,319,143,78,666,662,682,664 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#90fd68087a2f09648803d65723dcc8788b62f036d4e0ed1478893fb37d6a20cd, 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 19:12:59 · history