Equation 677 Database

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Magma bcf8074704d0…

magma bcf8074704d0
Size
381
Isomorphism class hash
bcf8074704d0f8e96e32443b6c94bc133186aa969b13041af4432b09d62dde15
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 23:16:33
Display reorder
380,15,14,16,17,18,13,24,19,20,21,22,23,315,316,317,312,313,314,217,222,227,232,237,212,207,182,187,192,197,202,157,162,167,172,177,152,292,297,272,277,282,287,242,247,252,257,262,267,29,30,25,26,27,28,11,12,7,8,9,10,0,6,2,3,4,5,339,336,332,338,351,363,358,368,377,372,92,91,93,94,89,90,98,99,100,95,96,97,303,304,305,301,300,302,218,223,228,233,238,213,208,183,188,193,198,203,158,163,168,173,178,153,293,298,273,278,283,288,243,248,253,258,263,268,110,111,112,107,108,109,115,116,117,118,113,114,106,105,101,102,103,104,347,334,345,346,352,361,355,366,379,370,145,144,146,147,148,143,121,122,123,124,119,120,327,328,329,324,325,326,219,224,229,234,239,214,209,184,189,194,199,204,159,164,169,174,179,154,294,299,274,279,284,289,244,249,254,259,264,269,136,131,132,133,134,135,141,142,137,138,139,140,128,127,129,130,125,126,330,333,349,348,353,364,357,367,378,373,69,68,70,71,72,67,149,73,74,75,76,1,321,322,323,318,319,320,215,220,225,230,235,211,205,181,185,190,195,200,156,160,165,170,175,151,290,295,271,276,281,286,241,246,251,256,261,265,87,88,83,84,85,86,65,66,61,62,63,64,81,80,82,77,78,79,344,335,340,343,354,360,359,369,376,371,51,50,52,53,54,49,60,55,56,57,58,59,311,306,307,308,309,310,216,221,226,231,236,210,206,180,186,191,196,201,155,161,166,171,176,150,291,296,270,275,280,285,240,245,250,255,260,266,42,37,38,39,40,41,47,48,43,44,45,46,34,33,35,36,31,32,342,337,341,331,350,362,356,365,375,374 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 = {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 23:16:34 · history