Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma cee257c38fd2…

magma cee257c38fd2
Size
705
Isomorphism class hash
cee257c38fd2aff915abdf6b6b8411c586371af7726b168cbd264fbe6024462a
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 15:34:05
Display reorder
660,415,414,416,417,418,419,412,413,411,408,409,410,421,422,420,424,425,423,427,428,426,430,431,429,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,394,395,393,390,391,392,385,386,384,388,389,387,689,694,699,700,570,572,571,575,573,574,567,568,569,566,564,565,579,580,581,578,576,577,585,586,587,584,582,583,593,591,592,589,590,588,599,597,598,595,596,594,560,558,559,563,561,562,555,556,557,554,552,553,546,547,548,549,550,551,544,545,543,540,541,542,688,691,696,703,613,612,614,615,616,617,618,619,620,621,622,623,625,626,624,628,629,627,631,632,630,634,635,633,637,638,636,640,641,639,643,644,642,646,647,645,601,602,600,604,605,603,607,608,606,610,611,609,94,95,93,90,91,92,85,86,84,88,89,87,664,672,674,673,234,236,235,239,237,238,231,232,233,230,228,229,245,243,244,241,242,240,251,249,250,247,248,246,212,210,211,215,213,214,207,208,209,206,204,205,224,222,223,227,225,226,219,220,221,218,216,217,490,491,489,486,487,488,481,482,480,484,485,483,663,679,683,682,119,118,117,114,115,116,109,110,108,112,113,111,131,129,130,127,128,126,122,120,121,125,123,124,141,142,143,140,138,139,132,133,134,135,136,137,103,104,102,106,107,105,101,99,100,97,98,96,45,46,47,44,42,43,36,37,38,39,40,41,687,690,695,702,307,306,308,309,310,311,304,305,303,300,301,302,313,314,312,316,317,315,319,320,318,322,323,321,326,324,325,329,327,328,332,330,331,335,333,334,652,653,651,648,649,650,658,659,657,654,655,656,30,31,32,33,34,35,28,29,27,24,25,26,686,685,698,701,285,287,286,283,284,282,278,276,277,281,279,280,298,299,297,294,295,296,289,290,288,292,293,291,259,260,258,262,263,261,257,255,256,253,254,252,271,272,270,274,275,273,269,267,268,265,266,264,48,49,50,51,52,53,54,55,56,57,58,59,692,693,697,704,538,537,539,536,534,535,528,529,530,531,532,533,499,500,498,502,503,501,497,495,496,493,494,492,511,512,510,514,515,513,509,507,508,505,506,504,523,524,522,526,527,525,521,519,520,517,518,516,74,72,73,77,75,76,80,78,79,83,81,82,665,680,684,681,383,382,381,378,379,380,373,374,372,376,377,375,340,341,339,336,337,338,346,347,345,342,343,344,352,353,351,348,349,350,358,359,357,354,355,356,365,363,364,361,362,360,371,369,370,367,368,366,4,5,3,1,0,2,10,11,9,6,7,8,662,667,668,678,196,195,197,194,192,193,201,202,203,200,198,199,463,464,462,466,467,465,461,459,460,457,458,456,476,474,475,479,477,478,471,472,473,470,468,469,398,396,397,401,399,400,404,402,403,407,405,406,16,17,15,12,13,14,22,23,21,18,19,20,661,676,675,677,165,167,166,163,164,162,158,156,157,161,159,160,179,177,178,175,176,174,170,168,169,173,171,172,189,190,191,188,186,187,180,181,182,183,184,185,146,144,145,149,147,148,152,150,151,155,153,154,64,65,63,60,61,62,70,71,69,66,67,68,666,670,669,671 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 15:34:07 · history