Equation 677 Database

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Magma ffddc7dc511e…

magma ffddc7dc511e
Size
381
Isomorphism class hash
ffddc7dc511e6de251601808382cac350db016fcccc2a91b04291711e409351b
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 23:16:50
Display reorder
380,102,107,103,104,105,106,320,321,322,317,318,319,115,116,117,118,119,114,193,198,203,208,183,188,100,101,96,97,98,99,5,1,0,2,3,4,238,213,218,223,228,233,168,173,178,153,158,163,110,111,112,113,108,109,248,253,258,263,268,243,288,283,293,298,273,278,347,346,377,342,364,372,367,340,358,359,125,124,120,121,122,123,312,313,314,315,316,311,141,142,143,138,139,140,191,196,200,205,181,186,144,145,146,147,148,149,129,130,131,126,127,128,235,211,216,221,226,230,165,170,175,151,156,161,137,132,133,134,135,136,246,251,256,260,265,241,286,281,290,295,271,276,337,357,378,334,361,373,368,331,335,350,56,55,57,58,59,54,308,309,310,307,306,329,42,43,44,45,46,47,190,195,201,206,180,185,53,48,49,50,51,52,65,60,61,62,63,64,236,210,215,220,225,231,166,171,176,150,155,160,39,40,41,36,37,38,245,250,255,261,266,240,285,280,291,296,270,275,354,332,379,345,362,374,369,355,348,353,29,28,24,25,26,27,303,304,305,301,300,302,15,16,17,12,13,14,192,197,202,207,182,187,18,19,20,21,22,23,33,34,35,30,31,32,237,212,217,222,227,232,167,172,177,152,157,162,11,6,7,8,9,10,247,252,257,262,267,242,287,282,292,297,272,277,351,349,375,339,363,371,365,352,338,341,74,73,75,76,77,72,327,328,323,324,325,326,92,93,94,95,90,91,194,199,204,209,184,189,71,66,67,68,69,70,83,78,79,80,81,82,239,214,219,224,229,234,169,174,179,154,159,164,84,85,86,87,88,89,249,254,259,264,269,244,289,284,294,299,274,279,336,330,376,333,360,370,366,344,356,343 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, M = {69} 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 23:16:51 · history