Equation 677 Database

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Magma bf488ba5afe2…

magma bf488ba5afe2
Size
705
Isomorphism class hash
bf488ba5afe20045a0a05e5b8160f2803f9ab0d66d6682700214db9802960a86
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 21:12:02
Display reorder
660,122,278,298,302,443,120,276,299,300,444,121,297,301,445,277,125,294,281,305,442,123,295,279,303,440,124,296,280,304,441,128,289,284,308,449,306,126,290,282,450,127,288,283,307,451,292,131,287,311,448,293,129,285,309,446,291,130,286,310,447,661,665,662,667,31,200,209,176,2,32,198,207,174,1,30,208,175,0,199,34,205,203,179,5,35,206,201,177,3,33,204,202,178,4,29,215,195,171,8,172,27,213,196,6,28,214,197,173,7,211,25,194,170,11,212,26,192,168,9,210,24,193,169,10,687,691,685,688,13,347,233,92,331,14,345,231,90,332,12,232,91,330,346,16,229,343,95,334,17,230,344,93,335,15,228,342,94,333,19,239,338,87,329,88,20,237,336,327,18,238,337,89,328,235,22,341,86,325,236,23,339,84,326,234,21,340,85,324,668,669,671,670,226,523,47,395,559,227,524,45,396,560,225,46,397,561,525,222,43,522,394,558,223,44,520,392,556,224,42,521,393,557,217,38,529,401,565,402,218,36,530,566,216,37,531,403,567,41,220,528,400,564,39,221,526,398,562,40,219,527,399,563,678,674,676,673,132,50,499,535,477,133,48,500,536,478,134,501,537,479,49,135,498,53,534,476,136,496,51,532,474,137,497,52,533,475,138,505,56,541,483,542,139,506,54,484,140,507,55,543,485,504,141,59,540,482,502,142,57,538,480,503,143,58,539,481,663,666,672,664,317,431,583,631,75,315,432,584,632,76,316,585,633,77,433,313,582,430,630,74,314,580,428,628,72,312,581,429,629,73,323,589,437,637,81,638,321,590,438,82,322,591,439,639,83,588,319,436,636,80,586,320,434,634,78,587,318,435,635,79,696,700,695,698,375,366,467,486,385,373,364,468,487,386,374,469,488,387,365,371,466,369,489,384,372,464,367,490,382,370,465,368,491,383,381,473,360,492,391,655,379,654,653,652,380,658,657,659,656,472,377,363,493,390,470,378,361,494,388,471,376,362,495,389,702,704,701,703,154,455,66,607,407,155,456,67,608,408,153,68,609,409,457,150,69,454,606,406,151,70,452,604,404,152,71,453,605,405,145,64,461,613,413,614,146,65,462,414,144,63,463,615,415,60,148,460,612,412,61,149,458,610,410,62,147,459,611,411,694,699,697,693,118,595,252,266,571,119,596,253,264,572,117,254,265,573,597,114,255,594,269,570,115,256,592,267,568,116,257,593,268,569,109,258,601,272,577,270,110,259,602,578,108,260,603,271,579,261,112,600,275,576,262,113,598,273,574,263,111,599,274,575,679,682,681,684,185,158,547,643,511,183,156,548,644,512,184,549,645,513,157,181,546,161,642,510,182,544,159,640,508,180,545,160,641,509,191,553,164,649,517,650,189,554,162,518,190,555,163,651,519,552,187,167,648,516,550,188,165,646,514,551,186,166,647,515,675,683,680,677,100,619,419,355,244,101,620,420,356,245,99,421,354,243,621,96,418,618,358,240,97,416,616,359,241,98,417,617,357,242,106,425,625,353,250,351,107,426,626,251,105,427,627,352,249,424,102,624,349,246,422,103,622,350,247,423,104,623,348,248,692,689,690,686 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#dcedbe28d6e821630efaff61054e89b4af79513af364c6246d7e9f07a2213221, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 21:12:03 · history