Equation 677 Database

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Magma bf01c29cd545…

magma bf01c29cd545
Size
381
Isomorphism class hash
bf01c29cd5454cf1a8094832b19dbaaa05a653094c1b8f4d515a2bbd803155d0
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 23:19:28
Display reorder
380,160,155,165,170,146,151,197,202,177,182,187,192,311,306,307,308,309,310,246,220,226,231,236,241,71,76,80,85,90,66,100,105,111,116,121,95,24,19,20,21,22,23,14,15,16,17,18,13,276,250,255,260,265,270,285,295,205,210,215,1,130,125,135,281,291,141,330,343,358,334,342,351,373,379,363,369,164,159,169,174,149,154,199,204,179,184,189,194,326,327,328,329,324,325,249,224,229,234,239,244,74,79,84,89,94,69,104,109,114,119,124,99,52,54,56,58,60,62,44,46,48,50,40,42,279,254,259,264,269,274,289,299,209,214,219,64,134,128,139,283,293,143,344,347,355,349,341,353,372,378,362,368,161,156,166,171,145,150,196,200,176,181,186,191,323,318,319,320,321,322,245,221,225,230,235,240,70,75,81,86,91,65,101,106,110,115,120,96,3,4,5,6,0,2,8,9,10,11,12,7,275,251,256,261,266,271,286,296,206,211,216,25,131,126,136,280,290,140,331,335,357,340,332,350,370,376,360,366,163,158,168,173,148,153,195,201,175,180,185,190,305,301,300,302,303,304,248,223,228,233,238,243,73,78,83,88,93,68,103,108,113,118,123,98,51,53,55,57,59,61,43,45,47,49,39,41,278,253,258,263,268,273,288,298,208,213,218,63,133,129,138,284,294,144,345,346,356,348,339,354,371,377,361,367,162,157,167,172,147,152,198,203,178,183,188,193,314,315,316,317,312,313,247,222,227,232,237,242,72,77,82,87,92,67,102,107,112,117,122,97,37,32,33,34,35,36,27,28,29,30,31,26,277,252,257,262,267,272,287,297,207,212,217,38,132,127,137,282,292,142,337,333,359,336,338,352,374,375,364,365 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#10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6, M = {74} 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 23:19:29 · history