Equation 677 Database

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Magma 586550c568da…

magma 586550c568da
Size
705
Isomorphism class hash
586550c568dabd5430a21692dca533670e235acb64bf072af8be48ce60305376
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 21:14:26
Display reorder
704,530,563,3,518,528,561,4,516,529,562,5,517,533,559,2,521,531,560,1,519,532,558,0,520,9,536,554,524,10,534,552,522,11,535,553,523,539,8,557,527,537,6,555,525,538,7,556,526,542,540,541,545,543,544,548,546,550,551,549,547,660,661,663,662,275,246,402,253,273,247,403,254,274,248,404,252,271,249,405,256,272,250,406,257,270,251,407,255,400,266,244,259,401,264,245,260,399,265,243,258,269,396,240,262,267,397,241,263,268,398,242,261,237,238,239,236,234,235,228,229,233,231,232,230,691,690,689,688,611,582,118,589,609,583,119,590,610,584,117,588,607,585,114,592,608,586,115,593,606,587,116,591,109,602,580,595,110,600,581,596,108,601,579,594,605,112,576,598,603,113,577,599,604,111,578,597,573,574,575,572,570,571,564,565,569,567,568,566,671,670,669,668,429,455,281,416,430,453,279,414,431,454,280,415,428,451,277,419,426,452,278,417,427,450,276,418,287,420,446,411,285,421,444,412,286,422,445,413,423,283,449,410,424,284,447,408,425,282,448,409,438,439,440,441,442,443,436,437,434,432,433,435,678,679,677,676,318,289,35,309,319,290,33,310,320,288,34,311,321,292,31,308,322,293,32,306,323,291,30,307,26,316,295,300,24,317,296,301,25,315,294,302,312,29,298,303,313,27,299,304,314,28,297,305,325,326,324,328,329,327,331,332,333,334,335,330,666,667,665,664,658,657,659,656,650,648,651,649,654,652,655,653,642,640,643,641,646,645,647,644,638,636,639,637,623,622,620,621,615,614,612,613,619,618,616,617,634,635,633,632,626,627,624,625,630,631,628,629,12,13,14,15,16,17,18,19,23,21,22,20,692,693,694,695,75,53,41,65,76,51,39,63,77,52,40,64,74,49,37,61,72,50,38,62,73,48,36,60,47,81,59,71,45,82,57,69,46,83,58,70,80,43,55,67,78,44,56,68,79,42,54,66,87,88,89,86,84,85,93,94,91,92,90,95,700,701,702,703,213,186,346,193,214,187,347,194,215,188,345,192,212,189,342,196,210,190,343,197,211,191,344,195,337,204,184,199,338,205,185,200,336,206,183,198,207,340,180,202,208,341,181,203,209,339,182,201,178,179,177,174,175,176,169,170,171,172,173,168,696,697,698,699,498,476,99,489,499,474,100,490,500,475,101,491,501,479,98,488,502,477,96,486,503,478,97,487,105,496,471,480,106,497,472,481,107,495,473,482,492,104,470,483,493,102,468,484,494,103,469,485,506,504,505,509,507,508,512,510,514,515,513,511,675,674,673,672,365,387,220,353,363,388,221,351,364,389,219,352,361,386,216,349,362,384,217,350,360,385,218,348,226,371,393,359,227,369,394,357,225,370,395,358,367,222,392,355,368,223,390,356,366,224,391,354,375,376,377,374,372,373,381,382,379,380,378,383,680,682,683,681,159,132,456,154,160,133,457,155,161,134,458,153,158,135,459,150,156,136,460,151,157,137,461,152,462,165,138,145,463,166,139,146,464,167,140,144,164,465,141,148,162,466,142,149,163,467,143,147,125,123,124,121,122,120,131,129,126,127,128,130,684,685,687,686 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#e051b0f30a8ed34180a71689094d032915fc358f2733da2908c1415c24d3cdbe, 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 21:14:27 · history