Equation 677 Database

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Magma 85baff21e5ae…

magma 85baff21e5ae
Size
381
Isomorphism class hash
85baff21e5aea9f28fc67a79de3a234e4c0af49aaa2478f2daf0d178843f889c
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 23:18:45
Display reorder
380,321,320,322,323,318,319,110,160,211,261,10,60,6,56,105,156,206,256,101,151,201,250,1,51,45,95,146,196,245,295,41,91,141,191,240,291,285,35,85,136,186,236,126,176,225,275,26,76,22,72,122,172,222,272,165,215,265,15,65,115,231,180,281,31,81,130,374,365,334,351,344,341,338,362,377,350,310,309,311,306,307,308,113,164,214,264,13,63,9,59,109,158,208,259,103,153,204,253,3,53,48,98,149,198,248,298,44,94,143,193,243,293,289,39,88,138,188,239,129,179,228,278,28,78,24,74,124,174,224,274,168,218,268,19,69,119,233,183,283,33,84,133,372,368,348,355,358,357,336,363,376,337,316,315,317,312,313,314,112,162,212,262,12,62,7,57,107,157,207,257,102,152,202,252,2,52,47,97,147,197,247,297,42,92,142,192,242,292,287,37,87,137,187,237,127,177,227,277,27,77,23,73,123,173,223,273,167,217,267,17,67,117,232,182,282,32,82,132,373,369,353,354,352,349,340,360,375,339,304,303,305,301,300,302,114,163,213,263,14,64,8,58,108,159,209,258,104,154,203,254,4,54,49,99,148,199,249,299,43,93,144,194,244,294,288,38,89,139,189,238,128,178,229,279,29,79,20,70,120,171,221,271,169,219,269,18,68,118,234,184,284,34,83,134,370,367,333,346,359,356,347,361,378,335,327,326,328,329,324,325,111,161,210,260,11,61,5,55,106,155,205,255,100,150,200,251,0,50,46,96,145,195,246,296,40,90,140,190,241,290,286,36,86,135,185,235,125,175,226,276,25,75,21,71,121,170,220,270,166,216,266,16,66,116,230,181,280,30,80,131,371,366,342,331,332,343,330,364,379,345 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 = {66} 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 23:18:46 · history