Equation 677 Database

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Magma 05665bbecd35…

magma 05665bbecd35
Size
381
Isomorphism class hash
05665bbecd3592c6405fa0b43db67a84c0a8bf8004874af3f882ea968c46c2fa
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 23:18:50
Display reorder
380,207,202,182,187,192,197,17,12,13,14,15,16,242,247,252,255,262,267,102,107,112,117,92,97,47,52,57,32,37,42,232,237,212,217,222,227,315,316,317,312,313,314,142,147,122,127,132,137,176,150,155,161,166,171,295,271,276,281,286,291,73,68,78,83,88,63,370,330,336,363,357,346,354,338,365,375,208,204,183,188,193,199,26,28,19,21,22,24,244,249,254,259,264,268,104,109,114,119,94,99,48,54,59,34,38,43,234,238,213,218,223,229,324,326,328,319,321,322,144,148,123,129,134,139,179,154,159,164,169,173,298,274,279,283,288,293,74,69,79,84,89,64,373,349,347,364,359,334,353,340,369,379,206,201,180,185,191,196,4,5,1,0,2,3,240,245,250,256,261,266,100,105,110,115,91,95,46,51,56,31,36,41,231,236,210,215,221,226,311,306,307,308,309,310,140,146,120,125,130,135,175,151,156,160,165,170,297,272,277,282,287,292,71,66,75,80,85,61,371,341,342,361,356,337,351,343,366,376,209,203,184,189,194,198,27,29,18,20,23,25,243,248,253,258,263,269,103,108,113,118,93,98,49,53,58,33,39,44,233,239,214,219,224,228,325,327,329,318,320,323,143,149,124,128,133,138,178,153,158,163,168,174,299,273,278,284,289,294,70,65,76,81,86,60,374,348,344,360,358,339,350,333,368,378,205,200,181,186,190,195,8,9,10,11,6,7,241,246,251,257,260,265,101,106,111,116,90,96,45,50,55,30,35,40,230,235,211,216,220,225,303,304,305,301,300,302,141,145,121,126,131,136,177,152,157,162,167,172,296,270,275,280,285,290,72,67,77,82,87,62,372,335,345,362,355,331,352,332,367,377 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 = {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 23:18:51 · history