Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 0379b2a23294…

magma 0379b2a23294
Size
381
Isomorphism class hash
0379b2a232944fab734c5f475798949375e9037b634e2b43c4c648d52db795be
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 23:21:04
Display reorder
380,279,268,289,299,249,259,130,131,126,127,128,129,64,65,60,61,62,63,80,81,82,83,78,79,197,207,217,227,237,187,76,77,72,73,74,75,125,120,121,122,123,124,266,277,287,297,247,257,239,189,199,209,219,229,301,300,302,303,304,305,70,71,66,67,68,69,342,341,352,368,351,343,377,344,365,379,275,269,285,295,245,255,8,9,10,11,6,7,36,37,38,39,40,41,99,100,101,96,97,98,192,202,212,222,232,182,102,103,104,105,106,107,2,3,4,5,1,0,262,272,282,292,242,252,235,185,195,205,215,225,311,306,307,308,309,310,45,46,47,42,43,44,337,338,332,364,331,347,372,348,362,375,271,261,280,290,241,251,144,145,146,147,148,149,48,49,50,51,52,53,18,19,20,21,22,23,193,203,213,223,233,183,17,12,13,14,15,16,155,150,151,152,153,154,263,273,283,293,243,253,231,180,191,201,211,221,314,315,316,317,312,313,57,58,59,54,55,56,339,340,354,361,355,333,373,334,367,371,270,260,281,291,240,250,174,175,176,177,178,179,28,29,24,25,26,27,159,160,161,156,157,158,198,208,218,228,238,188,162,163,164,165,166,167,172,173,168,169,170,171,267,278,288,298,248,258,230,181,190,200,210,220,329,324,325,326,327,328,34,35,30,31,32,33,336,335,359,360,358,356,378,357,369,370,274,264,284,294,244,254,109,110,111,112,113,108,91,92,93,94,95,90,139,140,141,142,143,138,196,206,216,226,236,186,133,134,135,136,137,132,118,119,114,115,116,117,265,276,286,296,246,256,234,184,194,204,214,224,320,321,322,323,318,319,89,84,85,86,87,88,346,345,350,366,349,330,376,353,363,374 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {73} 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 23:21:05 · history