Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 79cbd106f04a…

magma 79cbd106f04a
Size
381
Isomorphism class hash
79cbd106f04a64da620b31e42358b4070a9e83fbc4b1852e4314a7fc5e0fe3d2
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 301 (nullity 80) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:29:20
Display reorder
380,260,263,261,262,6,7,8,9,10,11,235,236,237,238,239,240,241,242,243,244,245,246,247,248,234,250,251,252,253,254,255,256,257,258,259,165,166,167,168,169,170,171,172,173,159,160,161,162,163,164,147,148,149,150,151,152,153,154,155,156,157,158,144,145,146,249,373,342,344,374,345,343,372,340,341,375,52,55,53,54,44,42,43,47,45,46,75,76,77,63,64,65,66,67,68,69,70,71,72,73,74,57,58,59,60,61,62,48,49,50,51,96,97,98,99,100,101,102,103,104,105,106,107,93,94,95,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,56,379,366,378,368,369,370,371,377,367,376,139,142,140,141,111,112,113,108,109,110,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,304,305,306,307,308,309,310,311,312,313,314,300,301,302,303,319,320,321,322,323,324,325,326,327,328,329,315,316,317,318,143,357,356,358,359,360,361,362,363,364,365,214,217,215,216,294,295,296,297,298,299,222,223,224,225,226,227,228,229,230,231,232,233,219,220,221,204,205,206,207,208,209,210,211,212,213,25,26,12,13,14,15,16,17,18,19,20,21,22,23,24,40,41,27,28,29,30,31,32,33,34,35,36,37,38,39,218,355,354,346,347,348,349,350,351,352,353,182,185,183,184,0,2,1,4,5,3,190,191,192,193,194,195,196,197,198,199,200,201,202,203,189,187,188,174,175,176,177,178,179,180,181,288,289,290,291,292,293,279,280,281,282,283,284,285,286,287,270,271,272,273,274,275,276,277,278,264,265,266,267,268,269,186,338,337,339,331,330,332,333,334,335,336 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#5e6aa1badf9e56cb7fdedb488e3ef1dcf34cbc2a2c9af577c3e3b36d4606ad9f, M = {76} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:29:21 · history