Equation 677 Database

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Magma 37765da6d0f7…

magma 37765da6d0f7
Size
705
Isomorphism class hash
37765da6d0f72ff5d169a2a85ab1f3b9a0e6f8b590e40b2b49f8b26463f2455c
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 16:57:01
Display reorder
660,299,393,141,489,107,300,394,142,490,105,301,392,143,488,106,302,389,140,485,103,303,390,138,486,104,304,391,139,487,102,297,399,147,495,113,298,400,148,496,111,296,398,149,494,112,395,293,146,491,109,396,294,144,492,110,397,295,145,493,108,663,666,672,668,195,513,37,127,45,196,514,38,128,46,194,512,36,126,47,191,509,40,130,44,192,510,41,131,42,193,511,39,129,43,186,519,35,133,51,187,520,33,134,52,185,518,34,132,53,515,189,31,136,50,516,190,32,137,48,517,188,30,135,49,687,690,688,689,246,585,549,321,429,247,586,550,322,430,245,584,548,320,428,249,581,545,317,425,250,582,546,318,426,248,583,547,319,427,252,591,555,327,435,253,592,556,328,436,251,590,554,326,434,587,255,551,323,431,588,256,552,324,432,589,254,553,325,433,671,670,664,662,203,345,417,573,537,204,346,418,574,538,205,344,416,572,536,206,341,413,569,533,207,342,414,570,534,208,343,415,571,535,201,351,423,579,543,202,352,424,580,544,200,350,422,578,542,347,197,419,575,539,348,198,420,576,540,349,199,421,577,541,675,678,680,683,220,501,477,453,119,218,502,478,454,117,219,500,476,452,118,216,497,473,449,115,217,498,474,450,116,215,499,475,451,114,211,507,483,459,125,209,508,484,460,123,210,506,482,458,124,503,214,479,455,121,504,212,480,456,122,505,213,481,457,120,669,667,661,665,309,381,74,405,561,310,382,72,406,562,308,380,73,404,560,305,377,77,401,557,306,378,75,402,558,307,379,76,403,559,315,387,69,411,567,316,388,70,412,568,314,386,71,410,566,383,311,68,407,563,384,312,66,408,564,385,313,67,409,565,694,693,696,695,150,162,532,597,2,151,634,635,632,633,152,166,531,596,0,153,163,528,593,5,154,164,529,594,3,155,165,530,595,4,156,653,652,654,655,157,657,656,658,659,158,649,648,650,651,637,159,636,638,639,641,160,640,642,643,645,161,644,646,647,701,703,704,702,90,168,527,602,231,91,169,525,603,232,92,167,526,601,230,93,171,523,598,227,94,172,524,599,228,95,170,522,600,229,96,629,628,608,222,97,631,630,609,223,98,627,626,607,221,1,99,521,604,225,623,100,622,605,226,625,101,624,606,224,699,700,697,698,58,269,614,283,357,59,270,615,281,358,57,271,613,282,356,54,272,610,286,353,55,273,611,284,354,56,274,612,285,355,64,275,620,289,363,65,276,621,287,364,63,277,619,288,362,278,60,616,292,359,279,61,617,290,360,280,62,618,291,361,682,684,676,673,238,369,333,182,465,236,370,334,183,466,237,368,332,184,464,234,365,329,181,461,235,366,330,179,462,233,367,331,180,463,244,375,339,173,471,242,376,340,174,472,243,374,338,175,470,371,240,335,176,467,372,241,336,177,468,373,239,337,178,469,677,674,679,681,29,441,7,267,84,27,442,8,268,85,28,440,6,266,86,25,437,10,263,87,26,438,11,264,88,24,439,9,265,89,20,447,13,258,82,18,448,14,259,83,19,446,12,257,81,443,23,16,261,78,444,21,17,262,79,445,22,15,260,80,686,685,691,692 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#49acd73e7fb20809c4c5aee6104079a0019ec0e0539c0b91c35b8b4466bd197d, 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 16:57:02 · history