Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma b2322471650d…

magma b2322471650d
Size
381
Isomorphism class hash
b2322471650d7c4fca6c86315d7f0d4ccc9588c4a0458bea451f4c3b63cdd275
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 23:34:04
Display reorder
380,42,47,43,44,45,46,231,246,261,276,291,216,32,33,34,35,30,31,259,274,289,214,229,244,38,39,40,41,36,37,314,315,316,317,312,313,26,27,28,29,24,25,171,186,201,126,141,156,148,163,178,193,208,133,223,238,253,268,283,298,184,169,199,124,139,154,335,352,337,378,336,355,334,362,371,369,97,96,98,99,100,101,235,250,265,280,295,220,111,112,113,108,109,110,257,272,287,212,227,242,104,105,106,107,102,103,311,306,307,308,309,310,117,118,119,114,115,116,175,190,205,130,145,160,143,158,173,188,203,128,218,233,248,263,278,293,182,167,197,122,137,152,349,351,346,373,347,358,348,357,375,365,23,22,18,19,20,21,225,240,255,271,286,210,73,74,75,76,77,72,267,282,297,222,237,252,16,17,12,13,14,15,323,318,319,320,321,322,82,83,78,79,80,81,165,180,195,121,135,150,140,155,170,185,200,125,215,230,245,260,275,290,192,177,207,132,147,162,342,360,333,370,332,363,343,353,366,377,62,61,63,64,65,60,234,249,264,279,294,219,91,92,93,94,95,90,258,273,288,213,228,243,66,67,68,69,70,71,301,300,302,303,304,305,87,88,89,84,85,86,174,189,204,129,144,159,136,151,166,181,196,120,211,226,241,256,270,285,183,168,198,123,138,153,344,354,340,367,341,361,345,350,374,368,5,4,1,0,2,3,236,251,266,281,296,221,58,59,54,55,56,57,269,284,299,224,239,254,9,10,11,6,7,8,328,329,324,325,326,327,53,48,49,50,51,52,176,191,206,131,146,161,142,157,172,187,202,127,217,232,247,262,277,292,194,179,209,134,149,164,338,364,330,372,331,359,339,356,376,379 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {74} 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 23:34:05 · history