Equation 677 Database

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Magma 3350b2a45df3…

magma 3350b2a45df3
Size
381
Isomorphism class hash
3350b2a45df3ae7f71f5c599e87c49a104960dc6f191cdaafb6e3e4e88840f16
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 23:36:50
Display reorder
380,323,322,321,319,318,63,53,58,278,68,73,320,178,183,188,193,198,203,123,118,288,113,103,108,298,173,168,158,163,153,8,13,3,267,23,17,138,128,133,148,143,293,213,218,208,228,233,223,48,273,43,33,38,28,83,283,78,98,88,93,248,238,243,263,253,258,333,372,353,363,358,368,338,348,343,378,324,326,325,329,328,61,51,56,276,65,70,327,176,181,186,190,195,201,120,115,286,111,100,106,295,171,166,155,160,151,5,10,0,266,22,15,135,126,131,146,141,290,210,215,206,226,230,221,47,272,42,32,37,27,80,280,76,95,86,90,247,236,241,262,251,257,331,374,350,360,356,365,337,346,342,375,317,316,315,313,312,60,50,55,275,66,71,314,175,182,187,192,197,202,121,116,285,110,101,105,296,170,165,156,161,150,7,12,2,265,21,19,136,125,130,145,140,291,212,217,207,227,232,222,46,270,41,30,35,26,81,281,75,96,85,91,246,237,242,261,252,256,330,370,351,361,355,366,335,345,340,376,307,306,308,309,311,62,52,57,277,67,72,310,177,180,185,191,196,200,122,117,287,112,102,107,297,172,167,157,162,152,6,11,1,268,20,16,137,127,132,147,142,292,211,216,205,225,231,220,45,271,40,31,36,25,82,282,77,97,87,92,245,235,240,260,250,255,332,371,352,362,357,367,336,347,341,377,304,303,305,301,302,64,54,59,279,69,74,300,179,184,189,194,199,204,124,119,289,114,104,109,299,174,169,159,164,154,9,14,4,269,24,18,139,129,134,149,144,294,214,219,209,229,234,224,49,274,44,34,39,29,84,284,79,99,89,94,249,239,244,264,254,259,334,373,354,364,359,369,339,349,344,379 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {68} 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 23:36:51 · history