Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 03a23dcc7b31…

magma 03a23dcc7b31
Size
705
Isomorphism class hash
03a23dcc7b31c6c0fd41eedcc66854c232afe7a9a1a95f5e6fc61867697cf2dc
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 19:56:52
Display reorder
660,56,629,632,635,630,652,54,655,650,649,612,55,609,615,610,552,59,549,555,550,569,57,572,575,570,592,58,589,595,590,447,450,451,51,448,469,472,475,52,470,429,432,435,53,430,512,509,515,50,510,532,529,535,48,530,49,492,489,495,490,698,689,692,687,237,636,637,628,627,657,238,648,647,656,617,239,616,608,607,557,236,556,548,547,576,234,577,568,567,597,235,596,588,587,452,453,446,228,445,476,477,468,229,467,436,437,428,230,427,517,516,508,231,507,537,536,528,232,527,233,497,496,488,487,697,693,701,699,101,406,418,358,310,419,99,359,311,407,417,100,405,357,309,414,97,402,354,306,403,98,415,355,307,416,96,404,356,308,397,409,349,107,301,398,410,350,105,302,396,408,348,106,300,412,400,352,103,304,413,401,353,104,305,102,411,399,351,303,672,667,682,681,27,382,394,346,298,395,28,347,299,383,393,29,381,345,297,390,26,378,342,294,379,24,391,343,295,392,25,380,344,296,373,385,337,33,289,374,386,338,34,290,372,384,336,35,288,388,376,340,32,292,389,377,341,30,293,31,387,375,339,291,670,666,678,674,91,639,638,631,623,659,92,651,643,658,618,90,619,611,603,558,94,559,551,543,579,95,578,571,563,599,93,598,591,583,458,459,449,89,442,479,478,471,87,463,439,438,431,88,424,519,518,511,85,504,539,538,531,86,524,84,499,498,491,484,691,686,695,700,199,621,634,620,626,654,200,640,646,641,614,198,601,600,606,554,202,541,540,546,561,203,574,560,566,594,201,580,581,586,456,457,440,197,441,461,474,460,195,466,421,434,420,196,426,514,501,500,193,506,534,521,520,194,526,192,494,481,480,486,688,685,696,694,215,622,633,624,625,653,213,644,645,642,613,214,602,604,605,553,211,542,544,545,562,212,573,564,565,593,210,582,584,585,454,455,443,206,444,462,473,464,204,465,423,433,422,205,425,513,503,502,209,505,533,523,522,207,525,208,493,483,482,485,704,702,703,690,130,322,150,274,74,151,131,275,72,323,152,129,321,273,73,153,126,318,270,77,319,127,154,271,75,155,128,320,272,76,313,148,265,121,80,314,149,266,122,78,312,147,264,120,79,144,316,268,124,83,145,317,269,125,81,123,146,315,267,82,664,676,662,668,67,334,262,37,286,263,68,38,287,335,261,66,333,36,285,258,70,330,40,282,331,71,259,41,283,260,69,332,39,284,325,253,43,65,277,326,254,44,63,278,324,252,42,64,276,256,328,46,61,280,257,329,47,62,281,60,255,327,45,279,675,665,663,669,223,247,14,5,370,12,224,3,371,248,13,222,246,4,369,17,226,250,0,366,251,227,15,2,367,16,225,249,1,368,245,20,11,221,361,243,18,9,219,362,244,19,10,220,360,23,241,7,217,364,21,242,8,218,365,216,22,240,6,363,684,673,683,677,133,184,118,168,164,119,134,169,162,185,117,132,183,170,163,114,136,180,171,167,181,137,115,172,165,116,135,182,173,166,190,109,174,139,159,191,110,175,140,160,189,108,176,138,161,112,186,177,142,158,113,187,178,143,156,141,111,188,179,157,661,679,671,680 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#b7ef46c52e3181531ee451cc516c519f12d29148a838b2a4381cb7ae279fb33d, 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 19:56:53 · history