Equation 677 Database

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Magma 09f80363493c…

magma 09f80363493c
Size
381
Isomorphism class hash
09f80363493c495810e7db698b7a830795590a53dc0f7506ca7c5d588c2bbb0b
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:43:50
Display reorder
380,97,145,274,114,279,280,98,146,275,115,281,99,147,270,116,100,276,148,271,117,101,277,149,272,118,144,278,96,273,119,51,191,209,325,121,186,52,204,323,122,187,53,205,324,123,48,188,206,329,124,49,189,207,322,125,50,190,208,326,120,255,257,252,253,254,256,363,332,339,364,342,334,366,333,365,367,105,40,286,128,155,153,106,41,287,129,154,107,36,282,130,102,150,37,283,131,103,152,38,284,126,39,151,104,285,127,133,192,289,301,5,193,134,290,300,1,194,135,291,315,0,136,195,292,302,2,137,196,293,303,3,132,197,288,304,4,263,259,260,261,262,258,376,337,345,377,346,350,374,349,373,375,72,44,244,84,162,163,73,45,245,85,164,74,46,240,86,75,165,47,241,87,76,166,42,242,88,43,167,77,243,89,111,202,269,309,12,203,112,264,305,13,198,113,265,327,14,108,199,266,306,15,109,200,267,307,16,110,201,268,308,17,230,232,233,228,229,231,358,340,341,360,331,338,362,330,361,355,33,81,222,66,296,297,34,82,223,67,298,35,83,224,68,30,299,78,225,69,31,294,79,226,70,80,295,32,227,71,92,235,246,312,140,236,93,247,313,141,237,94,248,314,142,95,238,249,328,143,90,239,250,310,138,91,234,251,311,139,185,181,182,183,184,180,370,344,348,371,336,343,368,335,372,369,26,9,214,56,173,168,27,10,215,57,169,28,11,210,58,29,170,6,211,59,24,171,7,212,54,8,172,25,213,55,60,157,220,321,23,158,61,221,316,18,159,62,216,317,19,63,160,217,318,20,64,161,218,319,21,65,156,219,320,22,176,178,179,174,175,177,379,354,347,359,351,352,357,353,356,378 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#cefabbfc99edd5b8e00d50ceabe10436bb4efcba7cfd32a2b0b9cb7036ac6db6, 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 23:43:51 · history