Equation 677 Database

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Magma 8d4a1169dbc3…

magma 8d4a1169dbc3
Size
705
Isomorphism class hash
8d4a1169dbc38319848d62daff63a4443940c164811d7e0f8cb84db9df18aa5a
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 21:13:27
Display reorder
704,199,83,104,62,60,81,200,102,61,82,198,103,202,65,79,107,203,63,80,105,64,201,78,106,74,68,99,197,72,66,100,195,73,67,101,196,71,77,98,193,69,75,96,194,70,76,97,192,90,91,92,93,94,95,88,89,86,84,85,87,675,673,674,672,370,522,498,515,513,523,371,499,514,524,369,500,366,511,525,501,367,512,526,502,510,368,527,503,520,506,496,361,521,504,497,362,519,505,495,360,509,516,492,364,507,517,493,365,508,518,494,363,539,537,538,535,536,534,530,528,532,533,531,529,664,666,665,667,45,112,212,222,223,113,46,210,224,111,47,211,44,225,108,215,42,226,109,213,227,43,110,214,118,220,207,36,119,221,208,37,117,219,209,38,216,114,206,39,217,115,204,40,218,116,205,41,648,649,650,651,652,653,654,655,658,656,657,659,685,686,684,687,296,330,308,320,318,331,294,306,319,332,295,307,299,323,333,311,297,321,334,309,322,298,335,310,328,315,303,291,329,316,304,292,327,317,305,293,314,324,302,290,312,325,300,288,313,326,301,289,345,346,347,344,342,343,336,337,341,339,340,338,701,703,700,702,389,593,626,647,645,591,387,624,646,592,388,625,385,643,589,629,386,644,590,627,642,384,588,628,599,638,632,395,597,636,630,393,598,637,631,394,641,595,635,391,639,596,633,392,640,594,634,390,600,601,602,603,604,605,606,607,611,609,610,608,688,689,690,691,34,280,263,271,272,281,35,261,270,279,33,262,30,274,276,259,31,275,277,260,273,32,278,258,286,269,254,25,287,267,252,26,285,268,253,24,265,282,257,28,266,283,255,29,264,284,256,27,240,241,242,243,244,245,246,247,251,249,250,248,662,661,663,660,23,409,437,396,397,410,21,435,398,408,22,436,19,399,412,433,20,400,413,434,401,18,411,432,415,402,443,14,416,403,441,12,414,404,442,13,405,418,439,17,406,419,440,15,407,417,438,16,430,431,429,426,427,428,421,422,423,424,425,420,694,693,695,692,237,612,143,55,56,613,238,141,54,614,239,142,236,58,615,139,234,59,616,140,57,235,617,138,618,53,134,228,619,51,132,229,620,52,133,230,49,621,137,231,50,622,135,232,48,623,136,233,120,121,122,123,124,125,126,127,131,129,130,128,682,683,681,680,352,489,461,469,470,490,353,459,468,491,351,460,348,472,488,457,349,473,486,458,471,350,487,456,480,475,467,358,481,476,465,359,482,474,466,357,478,483,463,354,479,484,464,355,477,485,462,356,455,453,454,451,452,450,446,444,448,449,447,445,696,698,699,697,379,562,578,541,542,563,380,576,540,561,378,577,382,544,558,581,383,545,559,579,543,381,560,580,553,547,584,377,554,548,582,375,552,546,583,376,550,556,587,373,551,557,585,374,549,555,586,372,567,568,569,566,564,565,573,574,571,572,570,575,671,668,670,669,7,168,151,159,160,169,8,152,161,170,6,150,10,158,171,154,11,156,172,155,157,9,173,153,174,165,149,5,175,166,147,3,176,167,148,4,164,177,145,0,162,178,146,2,163,179,144,1,180,181,182,183,184,185,186,187,191,189,190,188,676,678,677,679 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#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 21:13:28 · history