Equation 677 Database

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Magma 4431b4ad534f…

magma 4431b4ad534f
Size
381
Isomorphism class hash
4431b4ad534fbee4253b43820506f1fc90cc5174734b55b5dde428bf1567e4ea
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 23:33:16
Display reorder
380,14,13,15,16,17,12,261,266,240,246,251,256,18,71,22,19,20,21,39,40,35,36,37,38,155,160,165,170,176,150,216,221,226,231,236,210,23,24,25,26,27,28,271,276,281,286,291,296,33,34,29,30,31,32,313,314,315,316,329,312,201,196,191,206,180,186,364,366,346,345,332,340,371,376,331,344,73,72,74,75,76,77,264,269,243,249,254,259,79,80,81,82,83,78,96,97,98,99,100,101,158,163,168,173,179,153,219,224,229,234,239,213,86,87,88,89,84,85,273,279,284,289,294,299,92,93,94,95,90,91,301,300,302,303,304,305,204,199,194,209,183,189,360,369,351,350,347,338,374,379,335,333,55,54,56,57,58,53,262,267,242,247,252,257,59,60,61,62,63,64,48,49,50,51,52,47,157,162,167,172,177,152,217,222,227,232,237,212,70,65,66,67,68,69,272,277,282,287,292,297,41,42,43,44,45,46,311,306,307,308,309,310,202,197,192,207,182,187,362,365,359,343,341,349,370,375,339,342,10,9,11,6,7,8,263,268,244,248,253,258,142,143,138,139,140,141,137,132,133,134,135,136,159,164,169,174,178,154,218,223,228,233,238,214,148,149,144,145,146,147,274,278,283,288,293,298,129,130,131,126,127,128,323,324,325,326,327,328,203,198,193,208,184,188,363,368,357,334,354,356,373,378,358,355,111,110,112,113,108,109,260,265,241,245,250,255,116,117,118,119,114,115,105,106,107,102,103,104,156,161,166,171,175,151,215,220,225,230,235,211,1,0,2,3,4,5,270,275,280,285,290,295,123,124,125,120,121,122,317,318,319,320,321,322,200,195,190,205,181,185,361,367,330,336,353,337,372,377,348,352 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, M = {73} 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 23:33:17 · history