Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma c755afa4bc85…

magma c755afa4bc85
Size
381
Isomorphism class hash
c755afa4bc85cfa2da9bffe1f238d958e394a5c229613ea17a9ae2f2be83c5e5
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:33:24
Display reorder
380,165,161,170,175,151,156,43,44,45,46,47,42,48,49,50,51,52,53,241,246,251,255,260,265,236,210,216,221,226,231,196,201,206,180,185,190,40,41,36,37,38,39,316,317,312,313,314,315,285,290,296,270,275,280,61,62,63,64,65,60,56,55,54,57,58,59,356,343,370,336,344,362,340,334,375,365,169,163,174,179,154,158,24,25,26,27,28,29,32,33,34,35,30,31,244,248,253,258,263,269,238,213,218,223,229,233,199,204,209,184,188,193,23,18,19,20,21,22,308,309,310,311,306,307,288,293,299,274,278,283,8,9,10,11,6,7,16,15,14,17,12,13,358,338,373,331,339,364,341,342,378,369,166,160,171,176,150,155,88,89,84,85,86,87,94,95,90,91,92,93,240,245,250,256,261,266,235,211,215,220,225,230,195,200,205,181,186,191,78,79,80,81,82,83,300,302,303,304,305,301,286,291,295,271,276,281,74,75,76,77,72,73,71,70,69,66,67,68,357,332,372,335,330,361,346,345,377,366,168,164,173,178,153,159,120,121,122,123,124,125,105,106,107,102,103,104,243,249,254,259,264,268,239,214,219,224,228,234,198,203,208,183,189,194,119,114,115,116,117,118,322,323,318,319,320,321,289,294,298,273,279,284,1,0,2,3,4,5,112,111,110,113,108,109,359,350,374,349,333,363,337,351,379,368,167,162,172,177,152,157,144,145,146,147,148,149,129,130,131,126,127,128,242,247,252,257,262,267,237,212,217,222,227,232,197,202,207,182,187,192,143,138,139,140,141,142,328,329,324,325,326,327,287,292,297,272,277,282,99,100,101,96,97,98,136,135,134,137,132,133,355,353,371,352,348,360,347,354,376,367 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, M = {75} 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 23:33:25 · history