Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 18d3da6909ff…

magma 18d3da6909ff
Size
705
Isomorphism class hash
18d3da6909ff5fd8d3a0fdab271472c5df565905a48ca919e359f6062bffa664
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 20:08:56
Display reorder
660,281,108,587,492,383,282,109,588,493,384,110,280,589,494,385,277,111,586,491,382,278,112,584,489,380,279,113,585,490,381,114,272,578,483,374,115,273,579,484,375,116,271,580,485,376,275,117,581,486,377,276,118,582,487,378,274,119,583,488,379,663,666,671,669,480,344,575,185,188,481,345,576,186,189,346,482,577,184,187,479,347,574,181,191,477,348,572,182,192,478,349,573,183,190,342,471,566,176,194,343,472,567,177,195,341,473,568,175,193,474,338,569,179,197,475,339,570,180,198,476,340,571,178,196,685,690,686,688,635,50,563,504,81,636,48,564,505,82,49,637,565,506,83,634,53,562,503,80,632,51,560,501,78,633,52,561,502,79,56,626,554,495,72,54,627,555,496,73,55,628,556,497,74,629,59,557,498,75,630,57,558,499,76,631,58,559,500,77,662,667,672,668,428,35,350,516,418,426,30,351,517,419,33,427,352,518,417,424,24,353,515,421,425,29,354,513,422,423,25,355,514,420,46,434,356,507,416,42,432,357,508,414,44,433,358,509,415,430,38,359,510,412,431,40,360,511,413,429,36,361,512,411,675,677,684,681,444,201,371,611,468,445,199,372,612,469,200,446,373,613,470,443,204,370,610,467,441,202,368,608,465,442,203,369,609,466,207,435,362,602,459,205,436,363,603,460,206,437,364,604,461,438,210,365,605,462,439,208,366,606,463,440,209,367,607,464,665,670,664,661,599,70,2,456,125,600,71,1,457,123,69,601,0,458,124,598,66,5,455,121,596,67,3,453,122,597,68,4,454,120,61,590,8,447,131,62,591,6,448,129,60,592,7,449,130,593,64,11,450,127,594,65,9,451,128,595,63,10,452,126,693,695,698,696,647,164,537,153,541,655,165,654,653,652,163,659,656,658,657,646,167,538,156,146,644,168,539,154,144,645,166,540,155,145,170,638,535,159,149,171,639,536,157,147,169,640,534,158,148,641,173,531,162,152,642,174,532,160,150,643,172,533,161,151,702,703,704,701,283,139,408,551,392,648,140,409,552,649,138,651,410,553,650,396,142,407,550,393,397,143,405,548,394,398,141,406,549,395,137,289,399,542,390,135,287,400,543,391,136,288,401,544,389,285,133,402,545,386,286,134,403,546,387,284,132,404,547,388,700,697,699,694,254,96,264,528,623,255,97,262,529,624,98,253,263,530,625,257,99,260,527,622,258,100,261,525,620,256,101,259,526,621,102,252,270,519,614,103,250,268,520,615,104,251,269,521,616,248,105,266,522,617,249,106,267,523,618,247,107,265,524,619,683,678,679,673,331,14,293,313,315,329,12,294,311,316,13,330,295,312,314,327,17,292,309,318,328,15,290,310,319,326,16,291,308,317,20,337,299,304,321,18,335,300,302,322,19,336,301,303,320,333,23,298,307,324,334,21,296,305,325,332,22,297,306,323,676,674,680,682,233,34,236,94,217,234,31,237,95,218,32,232,235,93,219,229,27,239,90,220,230,28,240,91,221,231,26,238,92,222,47,224,242,85,215,43,225,243,86,216,45,223,241,84,214,227,39,245,88,211,228,41,246,89,212,226,37,244,87,213,687,692,689,691 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#ba8e767ab0f178377cc5ca58de8baa4e7db92c571ba3737b1b055d153a9d0c2e, 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 20:08:57 · history