Equation 677 Database

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Magma a54828236c0d…

magma a54828236c0d
Size
381
Isomorphism class hash
a54828236c0d752f91b583c487a70eeaaf35dc962b0600acf4e854e0e42f42ef
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 23:28:50
Display reorder
380,103,98,108,18,19,283,190,195,201,177,182,185,52,267,47,37,42,32,212,216,206,226,230,221,118,123,113,20,288,21,236,241,247,252,257,261,73,278,78,83,88,93,172,162,167,157,297,152,137,127,132,147,142,292,322,323,321,319,320,318,22,23,273,58,63,68,343,367,348,362,331,353,337,358,374,377,101,96,105,4,5,280,192,197,202,175,180,187,51,265,46,35,44,30,210,215,205,227,232,222,116,121,111,7,285,6,237,242,246,251,256,262,70,276,75,81,86,90,171,160,166,155,296,150,136,125,130,146,140,290,315,316,317,312,313,314,13,14,270,57,61,65,340,366,346,360,330,350,335,355,370,376,100,95,106,2,3,281,191,196,200,176,181,186,50,266,45,36,41,31,211,217,207,225,231,220,115,120,110,8,286,1,235,240,245,250,255,260,72,277,77,82,87,92,170,161,165,156,295,151,135,126,131,145,141,291,311,309,310,308,306,307,16,17,272,55,60,67,342,365,347,361,333,351,336,356,371,375,104,99,109,26,27,284,193,198,203,178,183,188,53,268,48,38,40,33,213,218,208,228,233,223,119,124,114,28,289,29,238,243,248,253,258,263,74,279,79,84,89,94,173,163,168,158,298,153,138,128,133,148,143,293,328,329,327,325,326,324,24,25,274,59,64,69,344,368,349,363,332,354,338,359,372,378,102,97,107,11,12,282,194,199,204,179,184,189,54,269,49,39,43,34,214,219,209,229,234,224,117,122,112,10,287,9,239,244,249,254,259,264,71,275,76,80,85,91,174,164,169,159,299,154,139,129,134,149,144,294,305,303,304,302,301,300,15,0,271,56,62,66,341,369,345,364,334,352,339,357,373,379 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#5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239, M = {71} 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 23:28:51 · history