Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 04023d6601bd…

magma 04023d6601bd
Size
705
Isomorphism class hash
04023d6601bd3803b528768bdaef99d0d8c29af4fce3eb2b3e042b3c8f205707
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 15:19:07
Display reorder
704,30,62,54,36,55,60,37,31,32,61,56,38,33,65,57,39,34,63,58,40,35,64,59,41,52,42,68,28,53,43,66,29,51,44,67,27,45,48,71,24,46,49,69,25,47,50,70,26,74,72,73,77,75,76,80,78,82,83,81,79,703,701,702,700,659,656,658,657,650,648,649,651,655,652,654,653,643,640,642,641,647,645,646,644,639,636,638,637,622,621,620,623,614,613,612,615,618,617,616,619,633,634,632,635,625,626,624,627,629,630,628,631,17,15,16,13,14,12,23,21,18,19,20,22,689,690,691,688,331,262,249,237,250,263,238,332,330,261,251,239,334,258,248,236,335,259,246,234,333,260,247,235,240,228,253,329,241,229,254,327,242,230,252,328,231,243,256,325,232,244,257,326,233,245,255,324,270,271,272,273,274,275,268,269,266,264,265,267,674,673,672,675,104,132,168,162,169,133,163,102,103,134,170,164,107,135,171,165,105,136,172,166,106,137,173,167,174,160,138,99,175,161,139,100,176,159,140,101,156,177,141,98,157,178,142,96,158,179,143,97,155,153,154,151,152,150,146,144,148,149,147,145,683,680,681,682,359,443,429,417,430,441,418,357,358,442,431,419,355,439,428,416,356,440,426,414,354,438,427,415,420,408,434,350,421,409,432,348,422,410,433,349,411,423,437,353,412,424,435,351,413,425,436,352,453,454,455,452,450,451,444,445,449,447,448,446,692,694,693,695,114,205,193,181,194,206,182,115,116,204,192,180,117,208,196,184,118,209,197,185,119,207,195,183,199,187,211,112,200,188,212,113,198,186,210,111,190,202,214,108,191,203,215,109,189,201,213,110,221,219,220,217,218,216,227,225,222,223,224,226,697,699,698,696,85,519,563,549,561,520,550,86,84,521,562,551,88,518,559,548,89,516,560,546,87,517,558,547,554,540,525,91,552,541,526,92,553,542,527,90,543,557,524,94,544,555,522,95,545,556,523,93,528,529,530,531,532,533,534,535,539,537,538,536,685,684,687,686,346,388,379,371,380,389,369,347,345,387,378,370,342,384,382,367,343,385,383,368,344,386,381,366,377,362,394,337,375,360,395,338,376,361,393,336,365,373,390,340,363,374,391,341,364,372,392,339,402,403,404,405,406,407,400,401,398,396,397,399,663,660,661,662,128,291,279,317,280,292,315,126,127,293,281,316,131,290,278,313,129,288,276,314,130,289,277,312,285,323,297,123,286,321,298,124,287,322,299,125,319,284,296,122,320,282,294,120,318,283,295,121,302,300,301,305,303,304,308,306,310,311,309,307,678,677,676,679,2,461,494,485,492,459,483,1,0,460,493,484,5,457,497,481,3,458,495,482,4,456,496,480,500,491,467,8,498,489,465,6,499,490,466,7,487,503,463,11,488,501,464,9,486,502,462,10,473,471,472,469,470,468,479,477,474,475,476,478,666,665,664,667,515,611,598,586,599,609,587,513,514,610,597,585,511,607,594,582,512,608,595,583,510,606,596,584,589,577,602,506,590,578,600,504,588,576,601,505,580,592,605,509,581,593,603,507,579,591,604,508,570,571,572,573,574,575,568,569,566,564,565,567,671,669,670,668 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#14697465b8cd7575930ebcd6f1cfb0d098649f4474b7abfd50cfc1485faac906, 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 15:19:08 · history