Equation 677 Database

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Magma e06bd9bac5b0…

magma e06bd9bac5b0
Size
381
Isomorphism class hash
e06bd9bac5b05f91551feeb1397c8c820822fe0aae2bfb7dda4924f477d6d619
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 23:19:03
Display reorder
380,81,76,86,61,66,71,175,151,156,160,165,170,19,20,21,22,23,18,314,315,316,317,312,313,205,181,186,191,196,200,250,256,261,266,240,245,290,295,271,276,281,285,36,41,46,51,55,31,91,96,101,106,111,115,235,211,215,220,225,230,145,140,121,126,131,135,358,345,332,375,337,344,362,366,370,351,84,79,89,63,69,74,178,154,159,164,169,174,5,1,0,2,3,4,328,319,321,322,324,326,209,183,188,193,198,203,253,258,264,269,243,248,294,299,273,278,283,289,38,43,48,53,59,34,93,99,104,109,114,119,239,213,218,223,228,234,149,144,123,128,134,139,355,334,347,376,341,338,364,369,371,353,82,77,87,62,67,72,176,150,155,161,166,171,12,13,14,15,16,17,304,305,301,300,302,303,206,180,185,190,195,201,251,255,260,265,241,246,291,296,270,275,280,286,35,40,45,50,56,30,90,95,100,105,110,116,236,210,216,221,226,231,146,141,120,125,130,136,357,340,336,378,339,342,361,367,373,352,83,78,88,64,68,73,179,153,158,163,168,173,8,9,10,11,6,7,329,318,320,323,325,327,208,184,189,194,199,204,254,259,263,268,244,249,293,298,274,279,284,288,39,44,49,54,58,33,94,98,103,108,113,118,238,214,219,224,229,233,148,143,124,129,133,138,356,343,349,377,348,346,363,368,372,354,80,75,85,60,65,70,177,152,157,162,167,172,25,26,27,28,29,24,311,306,307,308,309,310,207,182,187,192,197,202,252,257,262,267,242,247,292,297,272,277,282,287,37,42,47,52,57,32,92,97,102,107,112,117,237,212,217,222,227,232,147,142,122,127,132,137,359,335,330,379,333,331,360,365,374,350 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 = {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 23:19:04 · history