Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 04769667ebef…

magma 04769667ebef
Size
381
Isomorphism class hash
04769667ebef5600d5bf48ea4aa41cc41e2cb1b85a515ff3f696dd5c5814ba77
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 23:24:13
Display reorder
380,20,34,29,18,288,13,263,265,256,278,283,273,67,71,62,82,85,75,306,307,308,309,310,311,165,170,175,181,186,191,237,227,232,252,242,247,155,161,150,141,146,135,98,101,92,2,295,0,294,54,59,49,39,44,221,216,211,200,205,195,111,116,131,105,125,120,350,331,356,361,347,375,371,344,338,367,22,32,28,15,285,11,261,267,258,277,282,271,68,72,63,81,86,77,316,317,315,313,314,312,167,172,177,182,187,192,236,225,230,251,240,245,157,162,152,142,147,137,99,102,94,4,297,5,290,51,56,45,35,40,222,217,212,202,207,197,110,115,130,106,126,121,351,332,357,362,345,376,370,340,335,365,21,31,27,16,286,10,260,266,255,275,280,270,69,73,64,83,88,78,320,318,319,323,321,322,168,173,178,183,188,193,235,226,231,250,241,246,158,163,153,143,148,138,97,100,93,1,296,3,292,52,57,47,37,42,223,218,213,203,208,198,112,117,132,107,127,122,354,333,358,363,348,378,372,342,336,368,23,30,25,19,289,14,264,269,259,279,284,274,65,70,60,80,87,76,325,326,324,328,329,327,169,174,179,184,189,194,239,229,234,254,244,249,156,160,151,140,145,136,96,104,91,9,299,8,291,50,55,46,36,41,224,219,214,204,209,199,114,119,134,109,129,124,353,334,359,364,349,379,374,341,339,366,24,33,26,17,287,12,262,268,257,276,281,272,66,74,61,84,89,79,304,305,303,300,302,301,166,171,176,180,185,190,238,228,233,253,243,248,159,164,154,144,149,139,95,103,90,7,298,6,293,53,58,48,38,43,220,215,210,201,206,196,113,118,133,108,128,123,352,330,355,360,346,377,373,343,337,369 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#4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1, M = {69} 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 23:24:14 · history