Equation 677 Database

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Magma b0653215a51d…

magma b0653215a51d
Size
705
Isomorphism class hash
b0653215a51de72f0ee032bcbd1513e0e6661f5b79c4206fa3f9acc51a16c517
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 21:13:39
Display reorder
704,33,482,508,468,469,480,34,509,470,481,35,507,32,471,485,504,30,472,483,505,473,31,484,506,488,474,514,24,486,475,515,25,487,476,513,26,477,491,510,27,478,489,511,28,479,490,512,29,502,503,501,498,499,500,493,494,495,496,497,492,661,662,660,663,410,250,224,234,235,251,408,222,236,249,409,223,413,237,246,227,411,238,247,225,239,412,248,226,241,232,219,416,242,233,220,414,240,231,221,415,228,244,218,419,229,245,216,417,230,243,217,418,210,211,212,213,214,215,208,209,206,204,205,207,690,688,691,689,63,542,525,531,532,540,64,526,533,541,65,527,62,530,545,524,60,528,543,522,529,61,544,523,548,537,516,69,546,538,517,70,547,539,518,71,536,551,519,68,534,549,520,66,535,550,521,67,561,562,563,560,558,559,552,553,557,555,556,554,670,668,671,669,262,182,156,168,169,180,263,157,170,181,261,158,258,171,185,159,259,172,183,160,173,260,184,161,188,174,162,253,186,175,163,254,187,176,164,252,177,191,165,256,178,189,166,257,179,190,167,255,145,146,144,148,149,147,151,152,153,154,155,150,679,676,678,677,196,283,307,268,269,284,197,308,267,282,195,306,192,264,286,310,193,265,287,311,266,194,285,309,281,274,305,202,279,275,303,203,280,273,304,201,270,277,301,198,271,278,302,199,272,276,300,200,293,291,292,289,290,288,299,297,294,295,296,298,667,664,666,665,659,658,656,657,648,650,651,649,653,654,655,652,643,640,642,641,647,644,646,645,637,639,638,636,622,621,620,623,614,613,612,615,618,617,616,619,633,634,632,635,624,626,625,627,628,630,629,631,59,57,58,55,56,54,50,48,52,53,51,49,693,695,692,694,93,136,110,130,131,137,94,108,129,135,95,109,92,126,132,113,90,127,133,111,128,91,134,112,142,121,116,84,143,122,114,85,141,120,115,86,124,138,119,87,125,139,117,88,123,140,118,89,100,101,99,96,97,98,106,107,104,102,103,105,701,703,700,702,2,337,319,327,328,338,1,320,329,336,0,318,5,326,340,322,3,324,341,323,325,4,339,321,343,333,317,8,344,334,315,6,342,335,316,7,332,346,313,11,330,347,314,9,331,345,312,10,359,357,358,355,356,354,350,348,352,353,351,349,697,699,696,698,46,436,466,429,430,437,47,467,431,435,45,465,42,428,432,462,43,426,433,463,427,44,434,464,442,420,457,37,443,421,458,38,441,422,456,36,423,438,460,40,424,439,461,41,425,440,459,39,451,452,450,454,455,453,449,447,444,445,446,448,674,672,675,673,22,402,379,388,389,403,23,380,387,404,21,378,18,384,405,382,19,385,406,383,386,20,407,381,400,394,377,13,401,395,375,14,399,393,376,12,390,396,373,16,391,397,374,17,392,398,372,15,365,363,364,361,362,360,371,369,366,367,368,370,683,681,680,682,81,579,609,571,572,580,82,610,570,581,83,611,80,574,578,608,78,575,576,606,573,79,577,607,585,569,600,72,586,567,601,73,587,568,602,74,565,584,603,75,566,582,604,76,564,583,605,77,590,588,589,593,591,592,596,594,598,599,597,595,685,686,684,687 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#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 21:13:39 · history