Equation 677 Database

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Magma 46df89a7f55a…

magma 46df89a7f55a
Size
381
Isomorphism class hash
46df89a7f55a5d913bba6aa7e04b175ebb58efbcfdfe68ba3827080536ad1602
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 23:30:23
Display reorder
380,184,191,199,219,327,206,192,226,212,233,185,186,228,200,220,329,207,193,227,213,180,187,229,201,221,319,208,194,222,214,181,188,230,202,216,321,209,195,223,215,182,189,231,203,217,323,204,196,224,210,183,190,232,198,218,325,205,197,225,211,239,235,236,237,238,234,352,350,369,370,334,335,351,354,353,349,297,274,282,250,306,289,281,257,243,258,298,275,259,286,251,307,290,276,252,244,299,270,260,285,246,308,291,277,253,245,294,271,261,287,247,309,292,278,254,240,295,272,262,283,248,310,293,279,255,241,296,273,263,284,249,311,288,280,256,242,264,266,267,268,269,265,357,371,339,358,356,337,338,336,372,355,86,64,72,92,302,79,71,99,114,106,87,65,107,73,93,303,80,66,100,115,88,60,102,74,94,304,81,67,101,116,89,61,103,75,95,305,82,68,96,117,84,62,104,76,90,301,83,69,97,118,85,63,105,77,91,300,78,70,98,119,112,108,109,110,111,113,360,361,373,340,341,378,375,344,359,374,172,179,158,138,315,165,151,145,137,123,173,174,124,159,139,316,166,152,146,132,168,175,125,160,140,317,167,153,147,133,169,176,120,161,141,312,162,154,148,134,170,177,121,156,142,313,163,155,149,135,171,178,122,157,143,314,164,150,144,136,129,131,126,127,128,130,376,366,362,343,377,342,363,364,379,365,12,19,4,53,322,11,26,54,46,32,13,20,33,5,48,324,6,27,55,47,14,21,34,1,49,326,7,28,56,42,15,22,35,0,50,328,8,29,57,43,16,23,30,2,51,318,9,24,58,44,17,18,31,3,52,320,10,25,59,45,38,40,41,36,37,39,348,345,367,333,331,347,330,346,368,332 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#68a9b50691fe703ac73d06598244743c1485cfa9a6e73798a1481e5e49783ad7, 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 23:30:24 · history