Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 9992af576054…

magma 9992af576054
Size
705
Isomorphism class hash
9992af5760544378c000f697308037de0e6deb7eef5134f964d55e2a2bc8120f
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 15:32:12
Display reorder
660,506,507,63,503,508,64,527,523,526,528,487,486,65,483,488,62,427,422,426,428,451,60,449,450,452,61,467,462,466,468,69,627,622,626,628,70,647,642,646,648,71,607,602,606,608,547,68,542,546,548,567,66,562,566,568,587,67,582,586,588,698,690,686,685,510,514,283,513,512,284,534,533,530,532,494,490,282,493,492,286,434,433,430,432,458,287,457,456,447,285,474,473,470,472,281,634,633,630,632,279,654,653,650,652,280,614,613,610,612,554,277,553,550,552,574,278,573,570,572,594,276,593,590,592,688,687,691,693,316,244,153,400,292,154,245,401,317,293,243,315,155,399,291,152,240,396,312,288,241,150,397,313,289,151,242,398,314,290,144,250,406,322,298,145,251,407,323,299,146,249,405,321,297,246,147,402,318,294,247,148,403,319,295,248,149,404,320,296,665,667,678,661,170,260,198,388,225,199,258,389,168,226,259,169,200,387,227,201,263,384,173,224,261,202,385,171,222,203,262,386,172,223,196,255,394,176,216,197,256,395,174,217,195,257,393,175,218,254,192,390,179,219,252,193,391,177,220,253,194,392,178,221,671,664,676,662,504,509,3,505,511,4,529,525,524,531,489,484,5,485,491,2,429,425,424,431,445,1,444,443,446,0,469,465,464,471,9,629,625,624,631,10,649,645,644,651,11,609,605,604,611,549,8,545,544,551,569,6,565,564,571,589,7,585,584,591,689,702,696,703,519,517,53,518,502,51,538,537,539,522,497,499,52,498,482,49,437,438,439,423,441,50,440,442,448,48,477,478,479,463,59,638,637,639,623,57,658,657,659,643,58,618,617,619,603,558,55,557,559,543,577,56,578,579,563,598,54,597,599,583,694,701,697,700,500,516,72,501,515,73,536,521,520,535,496,480,74,481,495,75,436,420,421,435,459,76,455,454,453,77,476,461,460,475,78,636,621,620,635,79,656,641,640,655,80,616,601,600,615,556,81,540,541,555,576,82,560,561,575,596,83,580,581,595,692,704,695,699,103,118,232,123,136,233,119,124,104,137,117,102,231,125,135,228,114,122,106,132,115,229,120,107,133,230,116,121,105,134,238,109,129,101,142,239,110,130,99,143,237,108,131,100,141,112,234,128,97,138,113,235,126,98,139,111,236,127,96,140,680,683,675,679,187,352,210,164,376,211,353,162,188,377,351,186,212,163,375,213,348,167,190,372,349,214,165,191,373,215,350,166,189,374,208,358,159,185,382,209,359,160,183,383,207,357,161,184,381,354,204,158,181,378,355,205,156,182,379,356,206,157,180,380,674,681,684,672,41,304,264,340,26,265,305,341,39,24,303,40,266,339,25,267,300,336,37,29,301,268,337,38,27,269,302,338,36,28,270,310,346,47,32,271,311,347,45,30,272,309,345,46,31,306,273,342,43,35,307,274,343,44,33,308,275,344,42,34,670,677,669,666,328,364,91,412,12,92,365,413,329,13,363,327,90,411,14,94,360,408,324,15,361,95,409,325,16,93,362,410,326,17,89,370,418,334,18,87,371,419,335,19,88,369,417,333,20,366,85,414,330,21,367,86,415,331,22,368,84,416,332,23,663,668,682,673 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#1de75750e9587644a990145f0b96f270fc04381fd8036a009d6bb6ea07359c52, 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 15:32:13 · history