Equation 677 Database

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Magma d9cda290948a…

magma d9cda290948a
Size
705
Isomorphism class hash
d9cda290948a87d021c9bdd232c9fabe1595244cf125f558e334b0741e0759df
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 15:54:13
Display reorder
663,390,392,391,395,393,394,387,388,389,386,384,385,270,271,272,273,274,275,268,269,267,264,265,266,335,333,334,331,332,330,326,324,325,329,327,328,215,213,214,211,212,210,206,204,205,209,207,208,445,446,444,448,449,447,451,452,450,454,455,453,661,670,672,674,498,500,499,503,501,502,495,496,497,494,492,493,73,74,72,76,77,75,79,80,78,82,83,81,555,556,557,554,552,553,561,562,563,560,558,559,152,150,151,155,153,154,147,148,149,146,144,145,616,617,615,612,613,614,622,623,621,618,619,620,677,692,691,690,236,235,234,238,239,237,233,231,232,229,230,228,6,7,8,9,10,11,4,5,3,1,0,2,348,349,350,351,352,353,354,355,356,357,358,359,293,291,292,289,290,288,299,297,298,295,296,294,417,418,419,416,414,415,408,409,410,411,412,413,662,669,671,675,102,104,103,107,105,106,99,100,101,98,96,97,89,87,88,85,86,84,95,93,94,91,92,90,628,629,627,624,625,626,634,635,633,630,631,632,508,509,507,504,505,506,514,515,513,510,511,512,567,568,569,566,564,565,573,574,575,572,570,571,666,681,679,686,20,19,18,22,23,21,17,15,16,13,14,12,583,584,582,586,587,585,581,579,580,577,578,576,526,527,525,522,523,524,517,518,516,520,521,519,641,639,640,637,638,636,647,645,646,643,644,642,113,111,112,109,110,108,119,117,118,115,116,114,660,668,667,673,160,159,161,158,156,157,165,166,167,164,162,163,337,338,336,340,341,339,343,344,342,346,347,345,404,402,403,407,405,406,399,400,401,398,396,397,287,285,286,283,284,282,278,276,277,281,279,280,219,220,221,218,216,217,225,226,227,224,222,223,687,699,700,701,132,134,133,137,135,136,140,138,139,143,141,142,174,175,176,177,178,179,172,173,171,168,169,170,199,200,198,202,203,201,197,195,196,193,194,192,187,188,186,190,191,189,185,183,184,181,182,180,122,120,121,125,123,124,128,126,127,131,129,130,695,702,703,704,595,594,596,597,598,599,592,593,591,588,589,590,654,655,656,657,658,659,652,653,651,648,649,650,48,49,50,51,52,53,54,55,56,57,58,59,535,536,534,538,539,537,533,531,532,529,530,528,460,461,459,456,457,458,466,467,465,462,463,464,689,698,697,696,38,37,36,40,41,39,43,44,42,46,47,45,262,263,261,258,259,260,253,254,252,256,257,255,438,439,440,441,442,443,436,437,435,432,433,434,323,321,322,319,320,318,314,312,313,317,315,316,375,376,377,374,372,373,381,382,383,380,378,379,664,683,684,685,471,473,472,469,470,468,479,477,478,475,476,474,62,60,61,65,63,64,68,66,67,71,69,70,600,601,602,603,604,605,606,607,608,609,610,611,545,543,544,541,542,540,551,549,550,547,548,546,485,483,484,481,482,480,491,489,490,487,488,486,665,682,680,678,303,305,304,301,302,300,311,309,310,307,308,306,31,32,30,34,35,33,29,27,28,25,26,24,369,370,371,368,366,367,360,361,362,363,364,365,430,431,429,426,427,428,421,422,420,424,425,423,245,243,244,241,242,240,251,249,250,247,248,246,676,693,694,688 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {64} 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 15:54:15 · history