Equation 677 Database

← all  ·  ← by size  ·  ← size 399

Magma 048299857ea2…

magma 048299857ea2
Size
399
Isomorphism class hash
048299857ea26e0905c7d20e2625223e369e89a49238e8d4348584a35f47ee24
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
2026-10-07 09:13:10
Display reorder
144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,398,53,20,9,45,21,10,46,22,11,47,23,12,48,24,13,49,25,14,50,26,15,51,18,16,52,19,17,36,29,0,37,30,2,38,31,3,39,32,4,40,33,5,41,34,6,42,35,7,43,27,8,28,1,44,64,66,67,68,69,70,71,63,56,57,58,59,60,61,62,54,55,65,389,383,385,397,194,170,225,195,162,226,196,163,227,197,164,228,189,165,229,190,166,230,191,167,231,192,168,232,193,169,233,186,179,217,187,171,218,188,172,219,180,173,220,181,174,221,182,175,222,183,176,223,184,177,224,178,216,185,214,207,208,209,210,211,212,213,206,198,199,200,201,202,203,204,205,215,384,396,395,382,269,236,299,261,237,300,262,238,301,263,239,302,264,240,303,265,241,304,266,242,305,267,234,297,268,235,298,252,245,291,253,246,292,254,247,293,255,248,294,256,249,295,257,250,296,258,251,288,259,243,289,244,290,260,280,282,283,284,285,286,287,279,272,273,274,275,276,277,278,270,271,281,388,390,387,386,353,329,318,354,330,319,355,331,320,356,332,321,357,324,322,358,325,323,359,326,315,351,327,316,352,328,317,345,338,310,346,339,311,347,340,312,348,341,313,349,333,314,350,334,306,342,335,307,343,336,308,337,309,344,373,375,376,377,369,370,371,372,365,366,367,368,360,361,362,363,364,374,392,391,393,394,114,105,77,115,106,78,116,107,79,108,99,80,109,100,72,110,101,73,111,102,74,112,103,75,113,104,76,123,97,86,124,98,87,125,90,88,117,91,89,118,92,81,119,93,82,120,94,83,121,95,84,96,85,122,134,127,128,129,130,131,132,133,143,135,136,137,138,139,140,141,142,126,380,381,379,378 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#43f0c36223760e63518b60c236ae984455de73c5cc12b85e126b29cb91addc2f, 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 2026-10-07 09:13:12 · history