Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 882e8c7116a5…

magma 882e8c7116a5
Size
381
Isomorphism class hash
882e8c7116a5634000ae71af2a96465fe4c081684a22b8aa410f55f5b7c8456d
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 23:50:27
Display reorder
380,46,75,47,45,43,44,42,62,48,49,50,51,52,53,54,55,56,57,58,59,60,61,77,63,64,65,66,67,68,69,70,71,72,73,74,119,120,121,122,123,124,125,126,127,128,114,115,116,117,118,134,135,136,137,138,139,140,141,142,143,129,130,131,132,133,76,373,340,344,374,345,343,372,342,341,375,2,249,1,0,5,3,4,269,255,256,257,258,259,260,261,262,263,264,265,266,267,268,251,252,253,254,240,241,242,243,244,245,246,247,248,236,237,238,239,225,226,227,228,229,230,231,232,233,234,235,218,219,220,221,222,223,224,210,211,212,213,214,215,216,217,250,379,366,378,367,368,369,370,377,371,376,109,208,110,108,112,113,111,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,304,305,306,307,308,309,310,311,312,313,314,300,301,302,303,319,320,321,322,323,324,325,326,327,328,329,315,316,317,318,209,357,356,358,359,360,361,362,363,364,365,7,277,8,6,10,11,9,297,298,299,285,286,287,288,289,290,291,292,293,294,295,296,279,280,281,282,283,284,270,271,272,273,274,275,276,178,179,165,166,167,168,169,170,171,172,173,174,175,176,177,160,161,162,163,164,150,151,152,153,154,155,156,157,158,159,278,355,354,346,347,348,349,350,351,352,353,146,29,144,145,149,147,148,16,17,18,19,20,21,22,23,24,25,26,12,13,14,15,31,32,33,34,35,36,37,38,39,40,41,27,28,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,90,91,92,78,79,80,81,82,83,84,85,86,87,88,89,30,334,333,335,336,337,338,339,331,330,332 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#f59982e06fd8e46ca8a925a818bbbfbe68d94087e0cfa4cbef7756bcf9a9fdcb, 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 23:50:29 · history