Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma e5a110fc0843…

magma e5a110fc0843
Size
381
Isomorphism class hash
e5a110fc08431542feb31faac5ccd469a757655053950daf5e9c5f9385de8b84
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 23:19:07
Display reorder
380,111,106,116,90,95,101,311,312,313,314,315,316,225,231,236,210,215,220,290,296,270,275,280,285,36,40,45,50,55,31,150,155,160,165,171,176,65,71,76,81,86,60,245,250,256,261,266,240,201,206,180,186,191,196,9,10,11,6,7,8,125,120,130,135,141,146,363,365,345,353,336,373,338,335,356,378,113,108,118,93,98,104,300,302,303,304,305,301,228,234,239,214,218,223,293,299,274,279,283,288,38,44,48,53,58,33,154,158,163,168,174,179,68,74,78,83,88,63,246,251,255,260,265,241,204,208,183,189,194,199,18,20,22,24,27,29,128,124,133,138,144,149,362,367,347,352,341,372,344,333,358,377,110,105,115,91,96,100,320,321,317,329,318,319,226,230,235,211,216,221,291,295,271,276,281,286,35,41,46,51,56,30,151,156,161,166,170,175,66,70,75,80,85,61,247,252,257,262,267,242,200,205,181,185,190,195,14,15,16,17,12,13,126,121,131,136,140,145,357,366,348,351,337,370,332,330,355,375,114,109,119,94,99,103,322,323,324,325,326,327,229,233,238,213,219,224,294,298,273,278,284,289,39,43,49,54,59,34,153,159,164,169,173,178,69,73,79,84,89,64,248,253,258,263,268,243,203,209,184,188,193,198,19,21,23,25,26,28,129,123,134,139,143,148,364,369,349,350,342,374,343,334,360,379,112,107,117,92,97,102,328,308,309,310,307,306,227,232,237,212,217,222,292,297,272,277,282,287,37,42,47,52,57,32,152,157,162,167,172,177,67,72,77,82,87,62,249,254,259,264,269,244,202,207,182,187,192,197,5,1,0,2,3,4,127,122,132,137,142,147,361,368,346,354,339,371,331,340,359,376 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#10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6, 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 23:19:08 · history