Equation 677 Database

← all  ·  ← by size  ·  ← size 399

Magma 749a57e7c556…

magma 749a57e7c556
Size
399
Isomorphism class hash
749a57e7c556aaa21a16f405d1b4de77e3d7eb09c68c6fe7a3e653c4f9670887
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 19:14:09
Display reorder
11,12,13,14,15,16,17,9,10,3,4,5,6,7,8,1,0,2,398,95,123,153,154,96,124,155,97,125,156,98,117,157,90,118,158,91,119,92,159,120,160,93,121,94,161,122,104,145,115,105,146,116,106,147,108,107,148,109,99,149,110,100,150,111,101,151,112,102,152,113,103,144,114,143,136,137,138,139,140,141,142,126,127,128,129,130,131,132,133,134,135,389,383,385,397,250,252,293,294,251,253,295,243,254,296,244,255,288,245,256,289,246,257,247,290,258,291,248,259,249,292,260,242,302,261,234,303,262,235,304,263,236,305,264,237,297,265,238,298,266,239,299,267,240,300,268,241,301,269,272,274,275,276,277,278,270,271,281,282,283,284,285,286,287,279,280,273,384,396,395,382,187,215,174,175,188,207,176,180,208,177,181,209,178,182,210,179,183,211,184,171,212,172,185,213,186,173,214,196,166,198,197,167,199,189,168,200,190,169,201,191,170,202,192,162,203,193,163,204,194,164,205,195,165,206,227,229,230,231,232,233,225,226,219,220,221,222,223,224,216,217,218,228,388,390,387,386,325,353,323,315,326,354,316,327,355,317,328,356,318,329,357,319,330,358,331,320,359,321,332,351,324,322,352,334,306,345,335,307,346,336,308,347,337,309,348,338,310,349,339,311,350,340,312,342,341,313,343,333,314,344,373,375,376,377,369,370,371,372,365,366,367,368,360,361,362,363,364,374,392,391,393,394,51,62,23,24,52,54,25,53,55,26,45,56,18,46,57,19,47,58,48,20,59,21,49,60,50,22,61,43,32,71,44,33,63,36,34,64,37,35,65,38,27,66,39,28,67,40,29,68,41,30,69,42,31,70,73,75,76,77,78,79,80,72,82,83,84,85,86,87,88,89,81,74,378,380,381,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#2b16b18700a7ce59ce9ff679f011323add9234719de703a2caaf3de15033efc6, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-06 19:14:10 · history