Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma 2083dc628364…

magma 2083dc628364
Size
595
Isomorphism class hash
2083dc628364ab9afbb4340a54b1bbc6d69ca2ba0ba48b79d6050afc15219e66
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 11:55:11
Display reorder
64,63,65,60,61,62,351,319,344,321,322,320,331,330,332,335,333,334,365,364,363,360,361,362,339,341,340,343,350,342,514,511,510,516,577,241,243,244,245,240,242,153,152,154,155,150,151,267,266,268,269,264,265,124,123,125,120,121,122,252,257,253,254,255,256,146,145,147,148,149,144,3,2,4,5,1,0,66,71,67,68,69,70,185,184,180,181,182,183,89,88,84,85,86,87,396,395,394,392,393,391,379,378,380,381,382,383,390,389,388,387,385,386,359,358,357,354,355,356,467,468,504,505,470,469,306,462,424,461,423,460,534,533,527,524,532,525,579,556,548,557,549,554,581,550,563,576,12,14,15,16,17,13,272,271,273,274,275,270,138,143,139,140,141,142,131,130,126,127,128,129,302,300,303,304,305,301,112,111,113,108,109,110,170,169,171,172,173,168,209,208,204,205,206,207,18,23,19,20,21,22,285,284,286,287,282,283,429,430,353,482,500,481,491,501,492,490,488,489,509,487,499,486,454,453,483,443,442,439,440,441,327,329,328,325,326,324,323,463,425,464,426,465,542,535,540,541,523,519,594,560,561,582,591,555,592,586,590,589,104,106,107,102,103,105,199,198,200,201,202,203,226,225,227,222,223,224,81,80,82,83,78,79,133,132,134,135,136,137,296,295,297,298,299,294,163,162,164,165,166,167,247,246,248,249,250,251,6,11,7,8,9,10,72,77,73,74,75,76,348,352,349,347,345,346,316,318,317,315,313,314,403,402,401,400,398,399,411,412,413,416,414,415,476,475,506,397,507,477,480,405,479,508,478,404,536,537,513,522,521,529,593,588,568,567,578,585,572,571,558,570,43,45,46,41,42,44,95,94,90,91,92,93,37,36,38,39,40,35,27,26,28,25,24,53,50,49,51,52,47,48,34,33,29,30,31,32,97,96,98,99,100,101,157,156,158,159,160,161,197,196,192,193,194,195,280,279,281,276,277,278,466,428,427,338,336,337,368,367,366,370,371,369,406,408,407,409,410,438,450,484,417,485,451,452,310,312,311,308,309,307,422,420,502,498,503,421,531,543,517,518,526,512,566,544,552,551,559,583,545,584,565,546,59,55,56,57,58,54,187,186,188,189,190,191,221,220,216,217,218,219,230,229,231,232,233,228,174,179,175,176,177,178,259,258,260,261,262,263,293,292,288,289,290,291,115,114,116,117,118,119,239,238,234,235,236,237,214,213,215,210,211,212,474,437,436,435,434,473,493,456,455,419,459,497,447,449,448,444,445,446,431,471,384,472,432,433,374,373,372,375,376,377,418,496,458,494,457,495,539,538,530,515,520,528,562,580,587,564,553,574,569,573,575,547 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#967d317cf04778fc566aed88226f2ec73cf112a27da243deb50eb6f078cd5ea3, M = the submagma generated by {48, 78} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 11:55:12 · history