Equation 677 Database

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Magma e840112f8e26…

magma e840112f8e26
Size
381
Isomorphism class hash
e840112f8e269e7302df5524aae4025ced5cd87dfcab32cf51c9d64a291cde4d
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 23:24:37
Display reorder
380,325,324,326,327,328,329,294,194,239,144,44,94,258,158,249,108,8,58,284,184,229,134,39,84,164,209,264,14,64,114,234,289,189,89,139,33,199,244,298,49,99,149,169,214,269,19,69,119,74,124,24,219,274,174,279,224,179,79,129,29,109,9,159,59,259,204,349,359,344,364,369,374,379,339,354,338,310,309,311,306,307,308,293,191,236,140,41,92,250,150,245,101,1,50,282,182,227,132,37,82,162,207,262,12,62,112,232,287,187,85,136,31,195,241,295,46,95,146,167,212,267,17,67,117,72,122,22,217,272,172,276,221,176,75,125,27,105,5,155,55,255,202,347,356,342,362,367,371,375,335,352,330,316,315,317,312,313,314,290,192,237,142,42,93,254,154,247,104,4,54,281,181,226,130,35,80,161,205,260,10,60,110,231,286,186,87,137,30,197,242,297,47,97,147,165,211,266,15,65,115,70,120,20,216,270,171,277,222,177,77,127,25,103,3,153,52,252,200,346,357,340,361,366,370,377,332,350,334,301,302,300,305,303,304,292,193,238,143,40,90,257,157,248,107,7,57,283,183,228,133,38,83,163,208,263,13,63,113,233,288,188,88,138,32,198,243,299,48,98,148,168,213,268,18,68,118,73,123,23,218,273,173,278,223,178,78,128,28,106,6,156,56,256,203,348,358,343,363,368,373,378,336,353,337,322,321,323,318,319,320,291,190,235,141,43,91,251,152,246,102,2,51,280,180,225,131,36,81,160,206,261,11,61,111,230,285,185,86,135,34,196,240,296,45,96,145,166,210,265,16,66,116,71,121,21,215,271,170,275,220,175,76,126,26,100,0,151,53,253,201,345,355,341,360,365,372,376,333,351,331 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#4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1, M = {75} 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 23:24:38 · history