Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma db079dbd6084…

magma db079dbd6084
Size
381
Isomorphism class hash
db079dbd6084a9704209426873011e5960eee5d65f05491e41907f24649072a9
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 23:37:38
Display reorder
380,193,188,198,203,208,213,148,153,143,130,138,125,266,271,261,251,255,246,47,36,41,31,26,280,302,301,300,305,303,304,121,110,118,107,101,295,65,71,60,285,56,51,242,232,237,227,217,222,178,183,173,161,168,156,3,5,277,10,16,21,86,95,91,81,290,76,350,335,356,331,363,341,377,345,372,367,190,186,195,201,205,210,146,151,140,131,135,128,265,270,260,250,256,245,46,37,42,30,25,281,329,327,328,326,324,325,123,113,117,108,102,297,66,70,61,286,55,50,240,230,235,226,216,221,175,180,171,162,166,157,2,9,275,11,15,20,85,96,90,80,291,75,351,336,355,330,360,340,376,346,370,366,192,187,197,202,207,212,147,152,142,133,137,127,268,273,263,253,258,248,48,38,43,33,28,283,314,312,313,317,315,316,122,112,116,105,103,298,68,73,63,288,58,53,243,233,238,228,218,223,177,182,172,163,167,158,1,7,276,13,18,23,88,98,93,83,293,78,353,338,357,333,362,343,378,348,373,368,194,189,199,204,209,214,149,154,144,134,139,129,269,274,264,254,259,249,49,39,44,34,29,284,318,319,320,321,322,323,124,114,119,109,104,299,69,74,64,289,59,54,244,234,239,229,219,224,179,184,174,164,169,159,4,8,279,14,19,24,89,99,94,84,294,79,354,339,358,334,364,344,379,349,374,369,191,185,196,200,206,211,145,150,141,132,136,126,267,272,262,252,257,247,45,35,40,32,27,282,307,308,306,310,311,309,120,111,115,106,100,296,67,72,62,287,57,52,241,231,236,225,215,220,176,181,170,160,165,155,0,6,278,12,17,22,87,97,92,82,292,77,352,337,359,332,361,342,375,347,371,365 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, M = {68} 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 23:37:39 · history