Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma 1dd0687555f7…

magma 1dd0687555f7
Size
595
Isomorphism class hash
1dd0687555f73eff0810f3eff63dfd52e19e8f3e02a9d894072a2917ed4099c2
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
2026-10-06 20:09:05
Display reorder
71,70,66,67,68,69,14,13,12,15,16,17,177,179,178,174,175,176,400,399,401,396,397,398,377,376,372,373,374,375,512,538,520,567,561,33,35,34,30,31,32,37,36,38,41,39,40,140,139,138,141,142,155,159,161,160,158,156,157,195,191,187,183,256,253,228,227,226,229,230,231,246,245,244,247,248,249,119,118,117,116,114,115,408,413,409,410,411,412,473,472,468,469,470,471,326,325,327,328,329,324,338,337,339,340,341,336,406,405,407,402,403,404,318,323,319,320,321,322,415,414,416,417,418,419,426,431,427,428,429,430,534,552,528,543,514,549,516,535,584,579,585,560,566,555,565,564,215,214,216,218,219,217,239,238,240,243,241,242,250,254,180,193,185,189,106,105,107,102,103,104,108,110,109,111,112,113,125,124,123,120,121,122,49,48,50,53,51,52,204,203,202,207,205,206,451,450,452,453,454,455,485,484,480,481,482,483,495,494,496,497,492,493,437,436,432,433,434,435,445,444,446,447,448,449,275,274,270,271,272,273,334,333,335,330,331,332,263,262,259,258,260,261,540,539,545,527,547,529,551,526,591,571,586,589,580,575,577,574,43,42,44,46,47,45,151,150,149,152,153,154,129,131,130,127,128,126,64,63,65,60,61,62,55,54,56,58,59,57,10,9,11,8,6,7,74,72,73,75,76,77,148,147,146,145,143,144,293,292,288,289,290,291,489,488,490,491,486,487,478,477,479,474,475,476,381,380,382,383,378,379,503,502,498,499,500,501,351,350,352,353,348,349,283,282,284,285,286,287,464,463,465,466,467,462,530,521,532,518,517,511,533,519,594,583,572,556,554,559,573,590,233,232,234,236,237,235,199,201,200,197,198,196,252,257,181,194,186,190,96,98,97,95,93,94,173,172,171,170,168,169,21,23,22,19,20,18,25,24,26,29,27,28,166,165,167,163,164,162,425,424,420,421,422,423,305,304,300,301,302,303,442,441,443,438,439,440,386,385,387,388,389,384,266,265,267,268,269,264,311,310,306,307,308,309,315,314,316,317,312,313,295,294,296,297,298,299,541,515,536,537,550,513,544,524,593,563,568,587,569,576,570,578,85,84,86,100,101,99,81,83,82,79,80,78,87,89,88,91,92,90,1,2,0,5,3,4,192,188,184,182,255,251,212,211,213,210,208,209,225,224,223,220,221,222,136,135,137,133,134,132,356,355,357,358,359,354,505,504,506,507,508,509,461,460,456,457,458,459,343,342,344,345,346,347,362,361,363,364,365,360,370,369,371,366,367,368,276,281,277,278,279,280,393,392,394,395,390,391,523,548,531,542,525,546,522,510,553,562,592,582,558,581,557,588 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#141a5ad98d093a51cbcd8d0e5f762ac857a7d54b6447f4e2b6939d4d1af2e3e9, M = the submagma generated by {0, 42} (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 2026-10-06 20:09:06 · history