Equation 677 Database

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Magma ff644c53ed83…

magma ff644c53ed83
Size
705
Isomorphism class hash
ff644c53ed8321797ceafbd0a7141d2d80aa9e073c88a58a1be0a0e97b8db5be
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 21:13:16
Display reorder
704,457,483,514,477,478,484,458,515,479,485,456,513,460,476,482,510,461,474,480,511,475,459,481,512,489,468,505,463,490,469,506,464,491,470,504,462,471,488,508,466,472,486,509,467,473,487,507,465,494,492,493,497,495,496,500,498,502,503,501,499,703,702,700,701,659,658,657,656,649,650,651,648,653,654,655,652,643,640,642,641,647,644,646,645,637,639,638,636,622,620,621,623,614,612,613,615,618,616,617,619,633,634,632,635,624,626,625,627,628,630,629,631,2,1,0,5,3,4,8,6,10,11,9,7,690,688,691,689,306,113,143,152,150,111,307,141,151,112,308,142,309,155,109,139,310,153,110,140,154,311,108,138,119,147,134,304,117,148,132,305,118,149,133,303,146,115,137,300,144,116,135,301,145,114,136,302,120,121,122,123,124,125,126,127,131,129,130,128,674,673,675,672,380,402,427,435,436,403,378,428,437,404,379,426,383,434,405,430,381,432,406,431,433,382,407,429,400,441,425,375,401,442,423,376,399,443,424,377,440,396,421,374,438,397,422,372,439,398,420,373,417,418,419,416,414,415,408,409,413,411,412,410,680,682,681,683,12,248,223,232,233,246,13,224,231,247,14,222,15,228,251,226,16,229,249,227,230,17,250,225,243,238,221,18,244,239,219,19,245,237,220,20,234,242,217,21,235,240,218,22,236,241,216,23,210,211,212,213,214,215,208,209,206,204,205,207,694,695,693,692,390,341,369,333,334,339,391,370,335,340,392,371,393,332,337,368,394,330,338,366,331,395,336,367,347,324,360,388,345,325,361,389,346,326,362,387,327,343,363,384,328,344,364,385,329,342,365,386,348,349,350,351,352,353,354,355,359,357,358,356,699,696,698,697,450,529,560,519,520,530,451,558,521,528,452,559,453,518,532,563,454,516,533,561,517,455,531,562,535,525,555,448,536,526,556,449,534,527,557,447,524,538,554,444,522,539,552,445,523,537,553,446,549,550,551,548,546,547,540,541,545,543,544,542,687,685,686,684,102,185,162,178,179,183,103,163,177,184,104,164,105,174,181,165,106,175,182,166,176,107,180,167,191,169,160,100,189,170,161,101,190,168,159,99,172,187,156,96,173,188,157,97,171,186,158,98,193,194,192,196,197,195,199,200,201,202,203,198,660,662,661,663,323,294,272,284,282,295,321,270,283,296,322,271,319,287,297,275,320,285,298,273,286,318,299,274,292,279,267,314,293,280,268,312,291,281,269,313,278,288,266,317,276,289,264,315,277,290,265,316,258,259,260,261,262,263,256,257,254,252,253,255,677,679,676,678,94,37,65,74,72,38,95,63,73,36,93,64,90,77,40,61,91,75,41,62,76,92,39,60,43,80,71,85,44,78,69,86,42,79,70,84,83,46,67,88,81,47,68,89,82,45,66,87,59,57,58,55,56,54,50,48,52,53,51,49,664,666,665,667,29,587,604,570,571,585,27,605,572,586,28,603,25,573,583,600,26,574,584,601,575,24,582,602,578,568,610,35,576,569,611,33,577,567,609,34,564,581,606,31,565,579,607,32,566,580,608,30,596,594,595,599,597,598,591,592,589,590,588,593,669,668,670,671 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#df8d5557b781bba61b7abe058eca13be711d66cc8eaff0dccefd52d205bc7b58, 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 21:13:17 · history